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2026-02-13T15:28:57Z

Fuchs: /* KRESHNIK ANGONI'S LECTURES */

<big>'''Vanier College Physics Wiki'''</big>

Consult the [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.

== Getting started==
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]

==IMPORTANT DOCUMENTS==
Find your textbook, study guides and lab skills handbook here:
*[[STUDY DOCS]]



== MECHANICS ==
=== Introduction ===
* [http://stefan.bracher.info/files/physics/mechanics/mechanics_overview.pdf Mechanics Concept Overview]
* [http://stefan.bracher.info/files/physics/Formulas_and_Constants_for_College_Physics.pdf Stefan's Formulas for College Physics]
* [https://www.youtube.com/playlist?list=PLpDR89URs0h-zf-cHLTBNHUXOPYIEpWAg Stefan's Youtube Playlist for Mechanics]

=== Math review ===
==== Theory ====
* [http://stefan.bracher.info/files/physics/mechanics/Math_Review.pdf Stefan's Lecture Note on Math Review]

=== Measurement, Uncertainty, and Units ===
==== Videos ====
* [https://youtu.be/Kfy_Sd3jSCk Video: Introduction to uncertainties]
* [https://youtu.be/9YriBMqMx7c Video: Estimating the uncertainty of a measurement - Example: the length of a cat]
* [https://youtu.be/gHLzzzDohdE Video: Using the Min-Max Method to calculate the uncertainty of a measurement - Example: the length of a cat]
* [https://youtu.be/2ld3uFfRVt0 Video: Using the Average and Standard Deviation to calculate the uncertainty of a measurement - Example: the length of a cat]
* [https://youtu.be/e-Eb2wdZ-Qk Video: Accurate vs. Precise]
* [https://youtu.be/wyyBV3jnnZM?si=A8n01mY1oy_ffZ4W Video: An simple fix to improve the precision of a measurement]
* [https://youtu.be/7Q-zuT9cbeo Video: Calculations with uncertainty - Simple cases]
* [https://youtu.be/Lrkd6yHjTRI Video: Calculations with uncertainty - Complicated cases]
* [https://youtu.be/dumXDlANJA8 Video: Unit Conversion with dimensional analysis]
* [https://youtu.be/CLPjNelMLIs Video: Unit Conversion example: km/h to m/s]
* [https://youtu.be/7Vv7ExV87MU Video: SI-Prefixes]

==== Theory ====
* [http://gauss.vaniercollege.qc.ca/pwiki/index.php/Measurement_and_Data_Analysis Measurement and Data Analysis]
* [http://gauss.vaniercollege.qc.ca/pwiki/index.php/Uncertainties_in_Measurement Uncertainties in Measurement]
* [http://stefan.bracher.info/files/physics/mechanics/measurement_and_uncertainty.pdf Stefan's Lecture Note on Measurement and Uncertainty]

==== Book References ====
* [https://cnx.org/contents/1Q9uMg_a@13.38:bG-_rWXy@10/Introduction OpenStax University Physics Volume 1: Chapter 1.1-1.4]
* [https://cnx.org/contents/Ax2o07Ul@17.3:EC6WBNqn@13/1-2-Physical-Quantities-and-Units OpenStax College Physics: Chapter 1.2-1.3]

=== Vectors ===
==== Videos ====
* [https://youtu.be/jG6-AIGLOyM Video: Introduction to Vectors]
* [https://youtu.be/pDPOcpsdOXs Video: Drawing Vectors]
* [https://youtu.be/v2Cd4C7JXPY Video: Find the direction and the components of a vector]
* [https://youtu.be/OrryaQqcvk8 Video: Adding Vectors Graphically : Head to Tail Method]

==== Simulation ====
* [https://phet.colorado.edu/en/simulations/vector-addition Phet: Vector Addition]

==== Theory ====
* [[Vectors]]
* [http://stefan.bracher.info/files/physics/mechanics/Vectors.pdf Stefan's Lecture Note on Vectors]

==== Book References ====
* [https://cnx.org/contents/1Q9uMg_a@13.38:CEzSxrSw@8/Introduction Openstax University Physics Volume 1 - Chapter 2:Vectors]
* [https://cnx.org/contents/Ax2o07Ul@17.3:S9i77L2i@12/3-2-Vector-Addition-and-Subtraction-Graphical-Methods OpenStax College Physics - Chapter 3.2: Vector Addition and Subtraction: Graphical Methods]

=== Kinematics ===
*[[Basic Concepts]]

=====1 D Motion=====

====== Videos ======
* [https://youtu.be/g4s1j9nCyi4 Video: Introduction to Position-Time graphs]
* [https://youtu.be/YXrLMZb5uBA Video: Introduction to Velocity-Time graphs]
* [https://youtu.be/wArPnyyZCFg Video: Drawing the Position-Time graph from the Velocity-Time Graph]
* [https://youtu.be/wyZZn6sri5U Video: Kinematics Definitions, displacement, distance traveled, velocity and speed.]
* [http://stefan.bracher.info/files/physics/kinematics_formulas.htm Videos: Formulas for motion with constant acceleration]

* [https://youtu.be/-8eGB1WH0jw Video: Example - v-t, a-t and s-t graphs]
* [https://youtu.be/dKe0XFzSc6g Video: Example - Free-Fall]
* [https://youtu.be/q-TDxttAtLk Video: Example - Throwing an object in the air : Part 1]
* [https://youtu.be/nE5ePfnAyk8 Video: Example - Throwing an object in the air : Part 2]

* [https://youtu.be/22N1kAFx0L8 Video: Catch-up problems]

====== Theory ======
*[[Motion Along a Straight Line: Graphical Representation]] 
*[[Equations of Motion]]
* [[Free Fall]]

====== Simulation and practice ======
* [https://phet.colorado.edu/en/simulation/legacy/moving-man Simulation: Graphs]
* [https://www.geogebra.org/m/pdNj3DgD Geogebra: Create x-t and a-t graphs for various v-t graphs]
* [https://www.mathcelebrity.com/kinematic.php MathCelebrity: Kinematics Equations Calculator]

====== Book References ======
* [https://openstax.org/books/university-physics-volume-1/pages/3-introduction OpenStax University Physics Volume 1 - Chapter 3: Motion Along a Straight Line]
* [https://openstax.org/books/college-physics/pages/2-introduction-to-one-dimensional-kinematics OpenStax College Physics - Chapter 2: Introduction to One-Dimensional Kinematics]

=====2 D Motion=====
====== Videos ======
* [https://youtu.be/myHJ6_WS5OM Video: Introduction to 2D Kinematics]
* [https://youtu.be/_KyWgMUqP7k Video: Constant acceleration in 2D Kinematics]
* [https://youtu.be/tx8RMmVfy_E Video: Introduction to Projectile Motion]
* [https://youtu.be/x66EJxWhk8U Video: Projectile Motion Example - Angle and target location unknown]
* [https://youtu.be/vgUlurfyW0c Video: Projectile Motion Example - Maximal height and time to maximal height unknown]
* [https://youtu.be/qIi8-9rpRzU Video: Projectile Motion - Range and trajectory]
* [https://youtu.be/kwZ6_DAFFfE Video: Uniform Circular Motion - Centripetal Acceleration]

====== Theory ======
* [[Introduction to 2 D Motion]]
* [[Circular Motion]]
* [[Projectile Motion]]

====== Book References ======
* [https://openstax.org/books/university-physics-volume-1/pages/4-introduction OpenStax University Physics Volume 1 - Chapter 4: Motion in Two and Three Dimensions]
* [https://openstax.org/books/college-physics/pages/3-introduction-to-two-dimensional-kinematics OpenStax College Physics - Chapter 3: Introduction to Two-Dimensional Kinematics]

=====Rotational Kinematics=====
====== Videos ======
* [https://youtu.be/ZMZaO5mQLlE Video: Rotational Motion]
* [https://youtu.be/mwVww1NhIYk Video: Equations for constant angular acceleration]
* [https://youtu.be/3C4QfnlIQgM Video: Units of rotational motion (rpm)]
* [https://youtu.be/Nyv0SLEU2Aw Video: Rotational Kinematics Example]

====== Theory ======
* [[Rotational Motion]]


====== Book References ======
* [https://openstax.org/books/university-physics-volume-1/pages/10-introduction OpenStax University Physics Volume 1 - Chapter 10.1-10.3: Fixed-Axis Rotation]
* [https://openstax.org/books/college-physics/pages/10-introduction-to-rotational-motion-and-angular-momentum OpenStax College Physics - Chapter 10.1-10.2: Rotational Motion]

=== Dynamics ===
==== Videos ====
* [https://youtu.be/AUSXcozE_A0 Video: Introduction to Newton's Laws of Motion]
* [https://youtu.be/WzvhuQ5RWJE Video: Newton's 2nd Law of Motion]
* [https://youtu.be/cP0Bb3WXJ_k Video: Newton's 3rd Law of Motion]
* [https://youtu.be/dzdDzzRZm9U Video: Free Body Diagrams]
* [https://youtu.be/TLtGWls5F_I Video: Normal Forces Part 1]
* [https://youtu.be/JTeVBfUBdDs Video: Normal Forces Part 2]
* [https://youtu.be/t2RjGcvNSas Video: Tension Force]
* [https://youtu.be/dPSOs9lw90I Video: Simple Newton's Laws Problem Example]
* [https://youtu.be/ofeT2En6nz0 Video: Statics - Box on Surface]
* [https://youtu.be/R6ltYEMHuwc Video: Simple Dynamics Example]
* [https://youtu.be/pWsab45Httg Video: Two-body dynamics problem]
* [https://youtu.be/Y4FLaOTmklQ Video: Two boxes pushed along a surface]
* [https://youtu.be/JwEDFRDA5dc Video: Torque Shortcuts]
* [https://youtu.be/DMy6ree2sUA Video: Introduction to Rotational Equilibrium]
* [https://youtu.be/K1SxSdflCDA Video: Rotational and Translational Equilibrium - Beam with hanging mass]
* [https://youtu.be/XoAYWaDfs40 Video: Ladder leaning on the wall]
* [https://youtu.be/yC47CbcoWOE Video: Neil deGrasse Tyson: Einstein vs Newton - Who Was Right?]
* [https://youtu.be/lFgdmjmSxk0 Video: Newton's Universal Law of Gravity: Introduction]
* [https://youtu.be/xJqJ_UvBKiY Video: Newton's Universal Law of Gravity: Calculating the mass of the earth]
* [https://youtu.be/a-E28IqPVw8 Video: Newton's Universal Law of Gravity: Calculating the time it takes the moon to go around the earth]

==== Theory ====
*[[What is Dynamics?]]




*[[Inertia|The Concept of Inertia]] 
*[[Newton's Laws|Newton's Laws of Motion]] 
*[[Newton's Law of Universal Gravitation]] 
* [[Friction]]
*[[Dynamics of Circular Motion]] 
*[[Static and Dynamic Equilibrium]] 
*[[Torque]]


==== Book References ====
* [https://openstax.org/books/university-physics-volume-1/pages/5-introduction OpenStax University Physics Chapter 5: Newton's Laws of Motion]
* [https://openstax.org/books/university-physics-volume-1/pages/6-introduction OpenStax University Physics Chapter 6: Applications of Newton's Laws]
* [https://openstax.org/books/university-physics-volume-1/pages/10-6-torque OpenStax University Physics Chapter 10.6: Torque]
* [https://openstax.org/books/university-physics-volume-1/pages/10-7-newtons-second-law-for-rotation OpenStax University Physics Chapter 10.7: Newton's second law for rotation]

==== Simulations ====
* [https://phet.colorado.edu/en/simulation/forces-and-motion-basics Phet: Forces and Motion: Basics]
* [https://phet.colorado.edu/en/simulation/legacy/ramp-forces-and-motion Phet: Forces and Motion]
* [https://phet.colorado.edu/en/simulation/legacy/forces-and-motion Phet: Forces and Motion]
* [https://phet.colorado.edu/en/simulation/legacy/lunar-lander Phet: Lunar Lander]

=== Laws of Conservation ===
==== Videos - Basics of Conservation Laws ====
* [https://energy.ccdmd.qc.ca/videos/introduction-to-laws-of-conservation/ Video: Introduction to Laws of Conservation at CCDMD]
* [https://youtu.be/oDNAqnKhjZA Video: Introduction to Laws of Conservation (Conservation of Energy) by Stefan]

==== Videos - Energy ====
===== Videos - Conservation of Energy =====
* [https://energy.ccdmd.qc.ca/videos/introduction-to-conservation-of-energy/ Video: Introduction to Conservation of Energy at CCDMD]
* [https://energy.ccdmd.qc.ca/videos/conservation-of-energy-examples/ Video: Conservation of Energy Examples at CCDMD]

===== Videos - Energy in Mechanics =====
* [https://energy.ccdmd.qc.ca/videos/conservation-of-energy-in-mechanics/ CCDMD Video: Conservation of Energy in Mechanics]
* [https://youtu.be/a-4UISMSVpE Video: Conservation of Energy in Mechanics by Stefan]
* [https://energy.ccdmd.qc.ca/videos/conservation-of-energy-in-mechanics-exercise/ CCDMD Video: Conservation of Energy in Mechanics – Exercise]

===== Videos - Mechanical Work and Power =====
* [https://energy.ccdmd.qc.ca/videos/change-of-energy-through-mechanical-work/ CCDMD Video: Change of energy through mechanical work]
* [https://youtu.be/BEyZ60DHLnE Video: Mechanical Work by Stefan]
* [https://energy.ccdmd.qc.ca/videos/calculating-work-exercises/ CCDMD Video: Calculating work – Exercises]
* [https://energy.ccdmd.qc.ca/videos/introduction-to-power/ CCDMD Video: Introduction to Power]
* [https://energy.ccdmd.qc.ca/videos/power-exercise/ CCDMD Video: Power - Exercise]

===== Videos - Mechanical Energy =====
* [https://energy.ccdmd.qc.ca/videos/forms-of-energy-in-mechanics-discovery-of-kinetic-energy/ CCDMD Video: Forms of Energy in Mechanics: Discovery of Kinetic Energy]
* [https://energy.ccdmd.qc.ca/videos/forms-of-energy-in-mechanics-gravitational-potential-energy/ CCDMD Video: Forms of Energy in Mechanics: Gravitational Potential Energy]
* [https://energy.ccdmd.qc.ca/videos/forms-of-energy-in-mechanics-elastic-potential-energy/ CCDMD Video: Forms of Energy in Mechanics: Elastic Potential Energy]
* [https://youtu.be/y265HF0I1kg Video: Work required to lift an object (Discovery of Potential Energy) by Stefan]
* [https://youtu.be/a5qhsUWiZjw Video: Work required to accelerate an object to velocity v (Discovery of Kinetic Energy) by Stefan]
* [https://youtu.be/1XwxKKcn0ks Video: Conservative Forces and Potential Energy by Stefan]
* [https://youtu.be/CiSmPI4eHp8 Video: The potential energy of a spring by Stefan]
* [https://youtu.be/Jk9mYVAGHGk Video: Energy Example: Two connected blocks and a spring]
* [https://youtu.be/tGjZTRMSFBo Video: Energy Example: Calculating the escape velocity]
* [https://youtu.be/4HMXr7ExmBg Video: Pendulum Lab with Photogates - Conservation of Energy - Instructions]

===== Videos - Links to other courses (Chemistry, Thermodynamics, Applied Science, Engineering) =====
* [https://energy.ccdmd.qc.ca/videos/change-of-energy-through-heat/ CCDMD Video: Change of energy through heat]
* [https://energy.ccdmd.qc.ca/videos/thermal-energy/ CCDMD Video: Thermal Energy]
* [https://energy.ccdmd.qc.ca/videos/heat-machines/ CCDMD Video: Heat machines]
* [https://energy.ccdmd.qc.ca/videos/change-of-energy-through-heat-exercise/ CCDMD Video: Change of energy through heat – Exercise]
* [https://energy.ccdmd.qc.ca/videos/bernoullis-equation/ CCDMD Video: Bernoulli’s Equation (Fluid dynamics)]

===== Videos - Energy Review =====
* [https://energy.ccdmd.qc.ca/videos/popular-mistakes-with-conservation-of-energy/ CCDMD Video: Popular mistakes with conservation of energy]

==== Videos - Momentum ====
* [https://youtu.be/dNOthHSV0RM Video: Introduction to Linear Momentum]
* [https://youtu.be/I_RNxh8Eb-s Video: Conservation of Linear Momentum - Inelastic Collision]
* [https://youtu.be/ym2c6k09YY4 Video: Conservation of Linear Momentum - Example: 1D Inelastic Collision]
* [https://youtu.be/Fq7CasNQ_m0 Video: Conservation of Linear Momentum - Elastic Collision]
* [https://youtu.be/TArgOS55--I Video: Conservation of Linear Momentum - 2D Collision Example]
* [https://youtu.be/tXeQKIlxQEk Video: Conservation of Linear Momentum - Explosions]
* [https://youtu.be/zsMvyDSDPtI Video: Conservation of Linear Momentum - Rocket Equation (this is Rocket Science!)]
* [https://youtu.be/2FmyyHR47Xo Video: Conservation of Linear Momentum - Linear Momentum and Newton]
* [https://youtu.be/mqU9XBZ-jnw Video: Conservation of Angular Momentum - Introduction]
* [https://youtu.be/ULAar-EtJQI Video: Conservation of Angular Momentum - Changing the rotational inertia]
* [https://youtu.be/_RVe_ii-YJ4 Video: Conservation of Angular Momentum - A rotating platform]
* [https://www.youtube.com/watch?v=iaauRiRX4do Video: Conservation of Angular Momentum]

==== Theory ====
* [[Work and Energy]]

* [[Potential Energy]]

* [[Conservative and Non-Conservative Forces]]

* [[Conservation of Energy]]

* [[Rotational Kinetic Energy and Moment Of Inertia]]

* [[Conservation of Momentum|Conservation of Linear Momentum]] 

==== Book References ====
* [https://energy.ccdmd.qc.ca/glossary/ CCDMD: Glossary]
* [https://openstax.org/books/university-physics-volume-1/pages/7-introduction Openstax University Physics Volume 1: Chapter 7 (Work and Kinetic Energy)]
* [https://openstax.org/books/university-physics-volume-1/pages/8-introduction Openstax University Physics Volume 1: Chapter 8 (Potential Energy and Conservation of Energy)]
* [https://openstax.org/books/university-physics-volume-1/pages/9-introduction Openstax University Physics Volume 1: Chapter 9 (Linear Momentum and Collisions)]
* [https://openstax.org/books/university-physics-volume-1/pages/11-introduction Openstax University Physics Volume 1: Chapter 11 (Angular Momentum)]

=== Summary ===
* [https://youtu.be/3RnIH4_3E1U Video: Summary of Mechanics]

== STEFAN BRACHER'S LECTURES ==
*[http://stefan.bracher.info/physics_mechanics.php Stefan's Lecture notes for Mechanics]
 
== Interesting Articles on Mechanics ==

*[[My Daughter,the Physicist]]
:''by Stephen Cohen''

=====Felix Baumgartner's Sky Dive=====

[http://theengineerspulse.blogspot.ca/2012/10/mechanical-analysis-of-baumgartners.html Mechanical analysis of Baumgartner's sky dive]
 

[http://theengineerspulse.blogspot.ca/2012/10/mechanical-analysis-of-baumgartners_15.html Mechanical analysis of Baumgartner's sky dive-part 2]

 

== WAVES AND MODERN PHYSICS ==





*[[Waves and Modern Physics]] 

== ELECTRICITY AND MAGNETISM ==
*[[Electricity and Magnetism]] 






== 210 Electromechanics ==
*[[Electromechanics]]

== SECONDARY 5 PHYSICS ==
*[[Secondary 5 Physics]]

== REMEDIAL ACTIVITIES FOR SECONDARY 4 ENVIRONMENTAL SCIENCE AND TECHNOLOGY ==
*[[Secondary 4 Physical Science]]

== KEVIN LENTON'S MECHANICS MODULES ==

== KRESHNIK ANGONI'S LECTURES ==

* [http://gauss.vaniercollege.qc.ca/~physics/KRESHNIK_LECTURES/NYA Mechanics (SN1)] 
* [http://gauss.vaniercollege.qc.ca/~physics/KRESHNIK_LECTURES/Electricity_Magnetism Electricity & Magnetism (SN2)] 
* [http://gauss.vaniercollege.qc.ca/~physics/KRESHNIK_LECTURES/NYC Waves & Modern Physics (SN3)] 
 

== LABS: USEFUL MATERIAL==

* [http://www.lon-capa.org/~mmp/applist/sigfig/sig.htm Significant Figures] 

* [http://www.learnerstv.com/animation/animation.php?ani=94&cat=physics Reading a Micrometer Scale] 

* [[Uncertainties in Measurement]]
:''by Kreshnik Angoni''


* [[Measurement and Data Analysis]]
:''by Kreshnik Angoni''

* [[Preparation for Labs]]
:''by Helena Dedic''


 

==ADDITIONAL RESOURCES==
* [[The Exponential Function and Its Applications in Science]]
*:''by Don Hetherington''

* [http://theengineerspulse.blogspot.com/p/for-physics-students.html Physics articles organized by course subject]
*:''by Stephen Cohen''

* [[Study Skills]]

* [https://www.youtube.com/channel/UCpVm6r2eaxwTcSznVPm51AA/playlists Videos by Learning Commons on Various Topics like referencing and use of Office365]

===Career-Related Articles===
* [[Things I wish I knew before my first job]]
*:''by Scott Redmond''

* [[Choosing the Right Career Path]]
*:''by Scott Redmond''

==PHYSICS '''''FUN'''''==


*[[A Light in the Dark]]
 


== FOR TEACHERS ==

* [http://gauss.vaniercollege.qc.ca/twiki Teacher WIKI]

Main Page

2026-02-13T15:27:29Z

Fuchs: /* KRESHNIK ANGONI'S LECTURES */

<big>'''Vanier College Physics Wiki'''</big>

Consult the [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.

== Getting started==
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]

==IMPORTANT DOCUMENTS==
Find your textbook, study guides and lab skills handbook here:
*[[STUDY DOCS]]



== MECHANICS ==
=== Introduction ===
* [http://stefan.bracher.info/files/physics/mechanics/mechanics_overview.pdf Mechanics Concept Overview]
* [http://stefan.bracher.info/files/physics/Formulas_and_Constants_for_College_Physics.pdf Stefan's Formulas for College Physics]
* [https://www.youtube.com/playlist?list=PLpDR89URs0h-zf-cHLTBNHUXOPYIEpWAg Stefan's Youtube Playlist for Mechanics]

=== Math review ===
==== Theory ====
* [http://stefan.bracher.info/files/physics/mechanics/Math_Review.pdf Stefan's Lecture Note on Math Review]

=== Measurement, Uncertainty, and Units ===
==== Videos ====
* [https://youtu.be/Kfy_Sd3jSCk Video: Introduction to uncertainties]
* [https://youtu.be/9YriBMqMx7c Video: Estimating the uncertainty of a measurement - Example: the length of a cat]
* [https://youtu.be/gHLzzzDohdE Video: Using the Min-Max Method to calculate the uncertainty of a measurement - Example: the length of a cat]
* [https://youtu.be/2ld3uFfRVt0 Video: Using the Average and Standard Deviation to calculate the uncertainty of a measurement - Example: the length of a cat]
* [https://youtu.be/e-Eb2wdZ-Qk Video: Accurate vs. Precise]
* [https://youtu.be/wyyBV3jnnZM?si=A8n01mY1oy_ffZ4W Video: An simple fix to improve the precision of a measurement]
* [https://youtu.be/7Q-zuT9cbeo Video: Calculations with uncertainty - Simple cases]
* [https://youtu.be/Lrkd6yHjTRI Video: Calculations with uncertainty - Complicated cases]
* [https://youtu.be/dumXDlANJA8 Video: Unit Conversion with dimensional analysis]
* [https://youtu.be/CLPjNelMLIs Video: Unit Conversion example: km/h to m/s]
* [https://youtu.be/7Vv7ExV87MU Video: SI-Prefixes]

==== Theory ====
* [http://gauss.vaniercollege.qc.ca/pwiki/index.php/Measurement_and_Data_Analysis Measurement and Data Analysis]
* [http://gauss.vaniercollege.qc.ca/pwiki/index.php/Uncertainties_in_Measurement Uncertainties in Measurement]
* [http://stefan.bracher.info/files/physics/mechanics/measurement_and_uncertainty.pdf Stefan's Lecture Note on Measurement and Uncertainty]

==== Book References ====
* [https://cnx.org/contents/1Q9uMg_a@13.38:bG-_rWXy@10/Introduction OpenStax University Physics Volume 1: Chapter 1.1-1.4]
* [https://cnx.org/contents/Ax2o07Ul@17.3:EC6WBNqn@13/1-2-Physical-Quantities-and-Units OpenStax College Physics: Chapter 1.2-1.3]

=== Vectors ===
==== Videos ====
* [https://youtu.be/jG6-AIGLOyM Video: Introduction to Vectors]
* [https://youtu.be/pDPOcpsdOXs Video: Drawing Vectors]
* [https://youtu.be/v2Cd4C7JXPY Video: Find the direction and the components of a vector]
* [https://youtu.be/OrryaQqcvk8 Video: Adding Vectors Graphically : Head to Tail Method]

==== Simulation ====
* [https://phet.colorado.edu/en/simulations/vector-addition Phet: Vector Addition]

==== Theory ====
* [[Vectors]]
* [http://stefan.bracher.info/files/physics/mechanics/Vectors.pdf Stefan's Lecture Note on Vectors]

==== Book References ====
* [https://cnx.org/contents/1Q9uMg_a@13.38:CEzSxrSw@8/Introduction Openstax University Physics Volume 1 - Chapter 2:Vectors]
* [https://cnx.org/contents/Ax2o07Ul@17.3:S9i77L2i@12/3-2-Vector-Addition-and-Subtraction-Graphical-Methods OpenStax College Physics - Chapter 3.2: Vector Addition and Subtraction: Graphical Methods]

=== Kinematics ===
*[[Basic Concepts]]

=====1 D Motion=====

====== Videos ======
* [https://youtu.be/g4s1j9nCyi4 Video: Introduction to Position-Time graphs]
* [https://youtu.be/YXrLMZb5uBA Video: Introduction to Velocity-Time graphs]
* [https://youtu.be/wArPnyyZCFg Video: Drawing the Position-Time graph from the Velocity-Time Graph]
* [https://youtu.be/wyZZn6sri5U Video: Kinematics Definitions, displacement, distance traveled, velocity and speed.]
* [http://stefan.bracher.info/files/physics/kinematics_formulas.htm Videos: Formulas for motion with constant acceleration]

* [https://youtu.be/-8eGB1WH0jw Video: Example - v-t, a-t and s-t graphs]
* [https://youtu.be/dKe0XFzSc6g Video: Example - Free-Fall]
* [https://youtu.be/q-TDxttAtLk Video: Example - Throwing an object in the air : Part 1]
* [https://youtu.be/nE5ePfnAyk8 Video: Example - Throwing an object in the air : Part 2]

* [https://youtu.be/22N1kAFx0L8 Video: Catch-up problems]

====== Theory ======
*[[Motion Along a Straight Line: Graphical Representation]] 
*[[Equations of Motion]]
* [[Free Fall]]

====== Simulation and practice ======
* [https://phet.colorado.edu/en/simulation/legacy/moving-man Simulation: Graphs]
* [https://www.geogebra.org/m/pdNj3DgD Geogebra: Create x-t and a-t graphs for various v-t graphs]
* [https://www.mathcelebrity.com/kinematic.php MathCelebrity: Kinematics Equations Calculator]

====== Book References ======
* [https://openstax.org/books/university-physics-volume-1/pages/3-introduction OpenStax University Physics Volume 1 - Chapter 3: Motion Along a Straight Line]
* [https://openstax.org/books/college-physics/pages/2-introduction-to-one-dimensional-kinematics OpenStax College Physics - Chapter 2: Introduction to One-Dimensional Kinematics]

=====2 D Motion=====
====== Videos ======
* [https://youtu.be/myHJ6_WS5OM Video: Introduction to 2D Kinematics]
* [https://youtu.be/_KyWgMUqP7k Video: Constant acceleration in 2D Kinematics]
* [https://youtu.be/tx8RMmVfy_E Video: Introduction to Projectile Motion]
* [https://youtu.be/x66EJxWhk8U Video: Projectile Motion Example - Angle and target location unknown]
* [https://youtu.be/vgUlurfyW0c Video: Projectile Motion Example - Maximal height and time to maximal height unknown]
* [https://youtu.be/qIi8-9rpRzU Video: Projectile Motion - Range and trajectory]
* [https://youtu.be/kwZ6_DAFFfE Video: Uniform Circular Motion - Centripetal Acceleration]

====== Theory ======
* [[Introduction to 2 D Motion]]
* [[Circular Motion]]
* [[Projectile Motion]]

====== Book References ======
* [https://openstax.org/books/university-physics-volume-1/pages/4-introduction OpenStax University Physics Volume 1 - Chapter 4: Motion in Two and Three Dimensions]
* [https://openstax.org/books/college-physics/pages/3-introduction-to-two-dimensional-kinematics OpenStax College Physics - Chapter 3: Introduction to Two-Dimensional Kinematics]

=====Rotational Kinematics=====
====== Videos ======
* [https://youtu.be/ZMZaO5mQLlE Video: Rotational Motion]
* [https://youtu.be/mwVww1NhIYk Video: Equations for constant angular acceleration]
* [https://youtu.be/3C4QfnlIQgM Video: Units of rotational motion (rpm)]
* [https://youtu.be/Nyv0SLEU2Aw Video: Rotational Kinematics Example]

====== Theory ======
* [[Rotational Motion]]


====== Book References ======
* [https://openstax.org/books/university-physics-volume-1/pages/10-introduction OpenStax University Physics Volume 1 - Chapter 10.1-10.3: Fixed-Axis Rotation]
* [https://openstax.org/books/college-physics/pages/10-introduction-to-rotational-motion-and-angular-momentum OpenStax College Physics - Chapter 10.1-10.2: Rotational Motion]

=== Dynamics ===
==== Videos ====
* [https://youtu.be/AUSXcozE_A0 Video: Introduction to Newton's Laws of Motion]
* [https://youtu.be/WzvhuQ5RWJE Video: Newton's 2nd Law of Motion]
* [https://youtu.be/cP0Bb3WXJ_k Video: Newton's 3rd Law of Motion]
* [https://youtu.be/dzdDzzRZm9U Video: Free Body Diagrams]
* [https://youtu.be/TLtGWls5F_I Video: Normal Forces Part 1]
* [https://youtu.be/JTeVBfUBdDs Video: Normal Forces Part 2]
* [https://youtu.be/t2RjGcvNSas Video: Tension Force]
* [https://youtu.be/dPSOs9lw90I Video: Simple Newton's Laws Problem Example]
* [https://youtu.be/ofeT2En6nz0 Video: Statics - Box on Surface]
* [https://youtu.be/R6ltYEMHuwc Video: Simple Dynamics Example]
* [https://youtu.be/pWsab45Httg Video: Two-body dynamics problem]
* [https://youtu.be/Y4FLaOTmklQ Video: Two boxes pushed along a surface]
* [https://youtu.be/JwEDFRDA5dc Video: Torque Shortcuts]
* [https://youtu.be/DMy6ree2sUA Video: Introduction to Rotational Equilibrium]
* [https://youtu.be/K1SxSdflCDA Video: Rotational and Translational Equilibrium - Beam with hanging mass]
* [https://youtu.be/XoAYWaDfs40 Video: Ladder leaning on the wall]
* [https://youtu.be/yC47CbcoWOE Video: Neil deGrasse Tyson: Einstein vs Newton - Who Was Right?]
* [https://youtu.be/lFgdmjmSxk0 Video: Newton's Universal Law of Gravity: Introduction]
* [https://youtu.be/xJqJ_UvBKiY Video: Newton's Universal Law of Gravity: Calculating the mass of the earth]
* [https://youtu.be/a-E28IqPVw8 Video: Newton's Universal Law of Gravity: Calculating the time it takes the moon to go around the earth]

==== Theory ====
*[[What is Dynamics?]]




*[[Inertia|The Concept of Inertia]] 
*[[Newton's Laws|Newton's Laws of Motion]] 
*[[Newton's Law of Universal Gravitation]] 
* [[Friction]]
*[[Dynamics of Circular Motion]] 
*[[Static and Dynamic Equilibrium]] 
*[[Torque]]


==== Book References ====
* [https://openstax.org/books/university-physics-volume-1/pages/5-introduction OpenStax University Physics Chapter 5: Newton's Laws of Motion]
* [https://openstax.org/books/university-physics-volume-1/pages/6-introduction OpenStax University Physics Chapter 6: Applications of Newton's Laws]
* [https://openstax.org/books/university-physics-volume-1/pages/10-6-torque OpenStax University Physics Chapter 10.6: Torque]
* [https://openstax.org/books/university-physics-volume-1/pages/10-7-newtons-second-law-for-rotation OpenStax University Physics Chapter 10.7: Newton's second law for rotation]

==== Simulations ====
* [https://phet.colorado.edu/en/simulation/forces-and-motion-basics Phet: Forces and Motion: Basics]
* [https://phet.colorado.edu/en/simulation/legacy/ramp-forces-and-motion Phet: Forces and Motion]
* [https://phet.colorado.edu/en/simulation/legacy/forces-and-motion Phet: Forces and Motion]
* [https://phet.colorado.edu/en/simulation/legacy/lunar-lander Phet: Lunar Lander]

=== Laws of Conservation ===
==== Videos - Basics of Conservation Laws ====
* [https://energy.ccdmd.qc.ca/videos/introduction-to-laws-of-conservation/ Video: Introduction to Laws of Conservation at CCDMD]
* [https://youtu.be/oDNAqnKhjZA Video: Introduction to Laws of Conservation (Conservation of Energy) by Stefan]

==== Videos - Energy ====
===== Videos - Conservation of Energy =====
* [https://energy.ccdmd.qc.ca/videos/introduction-to-conservation-of-energy/ Video: Introduction to Conservation of Energy at CCDMD]
* [https://energy.ccdmd.qc.ca/videos/conservation-of-energy-examples/ Video: Conservation of Energy Examples at CCDMD]

===== Videos - Energy in Mechanics =====
* [https://energy.ccdmd.qc.ca/videos/conservation-of-energy-in-mechanics/ CCDMD Video: Conservation of Energy in Mechanics]
* [https://youtu.be/a-4UISMSVpE Video: Conservation of Energy in Mechanics by Stefan]
* [https://energy.ccdmd.qc.ca/videos/conservation-of-energy-in-mechanics-exercise/ CCDMD Video: Conservation of Energy in Mechanics – Exercise]

===== Videos - Mechanical Work and Power =====
* [https://energy.ccdmd.qc.ca/videos/change-of-energy-through-mechanical-work/ CCDMD Video: Change of energy through mechanical work]
* [https://youtu.be/BEyZ60DHLnE Video: Mechanical Work by Stefan]
* [https://energy.ccdmd.qc.ca/videos/calculating-work-exercises/ CCDMD Video: Calculating work – Exercises]
* [https://energy.ccdmd.qc.ca/videos/introduction-to-power/ CCDMD Video: Introduction to Power]
* [https://energy.ccdmd.qc.ca/videos/power-exercise/ CCDMD Video: Power - Exercise]

===== Videos - Mechanical Energy =====
* [https://energy.ccdmd.qc.ca/videos/forms-of-energy-in-mechanics-discovery-of-kinetic-energy/ CCDMD Video: Forms of Energy in Mechanics: Discovery of Kinetic Energy]
* [https://energy.ccdmd.qc.ca/videos/forms-of-energy-in-mechanics-gravitational-potential-energy/ CCDMD Video: Forms of Energy in Mechanics: Gravitational Potential Energy]
* [https://energy.ccdmd.qc.ca/videos/forms-of-energy-in-mechanics-elastic-potential-energy/ CCDMD Video: Forms of Energy in Mechanics: Elastic Potential Energy]
* [https://youtu.be/y265HF0I1kg Video: Work required to lift an object (Discovery of Potential Energy) by Stefan]
* [https://youtu.be/a5qhsUWiZjw Video: Work required to accelerate an object to velocity v (Discovery of Kinetic Energy) by Stefan]
* [https://youtu.be/1XwxKKcn0ks Video: Conservative Forces and Potential Energy by Stefan]
* [https://youtu.be/CiSmPI4eHp8 Video: The potential energy of a spring by Stefan]
* [https://youtu.be/Jk9mYVAGHGk Video: Energy Example: Two connected blocks and a spring]
* [https://youtu.be/tGjZTRMSFBo Video: Energy Example: Calculating the escape velocity]
* [https://youtu.be/4HMXr7ExmBg Video: Pendulum Lab with Photogates - Conservation of Energy - Instructions]

===== Videos - Links to other courses (Chemistry, Thermodynamics, Applied Science, Engineering) =====
* [https://energy.ccdmd.qc.ca/videos/change-of-energy-through-heat/ CCDMD Video: Change of energy through heat]
* [https://energy.ccdmd.qc.ca/videos/thermal-energy/ CCDMD Video: Thermal Energy]
* [https://energy.ccdmd.qc.ca/videos/heat-machines/ CCDMD Video: Heat machines]
* [https://energy.ccdmd.qc.ca/videos/change-of-energy-through-heat-exercise/ CCDMD Video: Change of energy through heat – Exercise]
* [https://energy.ccdmd.qc.ca/videos/bernoullis-equation/ CCDMD Video: Bernoulli’s Equation (Fluid dynamics)]

===== Videos - Energy Review =====
* [https://energy.ccdmd.qc.ca/videos/popular-mistakes-with-conservation-of-energy/ CCDMD Video: Popular mistakes with conservation of energy]

==== Videos - Momentum ====
* [https://youtu.be/dNOthHSV0RM Video: Introduction to Linear Momentum]
* [https://youtu.be/I_RNxh8Eb-s Video: Conservation of Linear Momentum - Inelastic Collision]
* [https://youtu.be/ym2c6k09YY4 Video: Conservation of Linear Momentum - Example: 1D Inelastic Collision]
* [https://youtu.be/Fq7CasNQ_m0 Video: Conservation of Linear Momentum - Elastic Collision]
* [https://youtu.be/TArgOS55--I Video: Conservation of Linear Momentum - 2D Collision Example]
* [https://youtu.be/tXeQKIlxQEk Video: Conservation of Linear Momentum - Explosions]
* [https://youtu.be/zsMvyDSDPtI Video: Conservation of Linear Momentum - Rocket Equation (this is Rocket Science!)]
* [https://youtu.be/2FmyyHR47Xo Video: Conservation of Linear Momentum - Linear Momentum and Newton]
* [https://youtu.be/mqU9XBZ-jnw Video: Conservation of Angular Momentum - Introduction]
* [https://youtu.be/ULAar-EtJQI Video: Conservation of Angular Momentum - Changing the rotational inertia]
* [https://youtu.be/_RVe_ii-YJ4 Video: Conservation of Angular Momentum - A rotating platform]
* [https://www.youtube.com/watch?v=iaauRiRX4do Video: Conservation of Angular Momentum]

==== Theory ====
* [[Work and Energy]]

* [[Potential Energy]]

* [[Conservative and Non-Conservative Forces]]

* [[Conservation of Energy]]

* [[Rotational Kinetic Energy and Moment Of Inertia]]

* [[Conservation of Momentum|Conservation of Linear Momentum]] 

==== Book References ====
* [https://energy.ccdmd.qc.ca/glossary/ CCDMD: Glossary]
* [https://openstax.org/books/university-physics-volume-1/pages/7-introduction Openstax University Physics Volume 1: Chapter 7 (Work and Kinetic Energy)]
* [https://openstax.org/books/university-physics-volume-1/pages/8-introduction Openstax University Physics Volume 1: Chapter 8 (Potential Energy and Conservation of Energy)]
* [https://openstax.org/books/university-physics-volume-1/pages/9-introduction Openstax University Physics Volume 1: Chapter 9 (Linear Momentum and Collisions)]
* [https://openstax.org/books/university-physics-volume-1/pages/11-introduction Openstax University Physics Volume 1: Chapter 11 (Angular Momentum)]

=== Summary ===
* [https://youtu.be/3RnIH4_3E1U Video: Summary of Mechanics]

== STEFAN BRACHER'S LECTURES ==
*[http://stefan.bracher.info/physics_mechanics.php Stefan's Lecture notes for Mechanics]
 
== Interesting Articles on Mechanics ==

*[[My Daughter,the Physicist]]
:''by Stephen Cohen''

=====Felix Baumgartner's Sky Dive=====

[http://theengineerspulse.blogspot.ca/2012/10/mechanical-analysis-of-baumgartners.html Mechanical analysis of Baumgartner's sky dive]
 

[http://theengineerspulse.blogspot.ca/2012/10/mechanical-analysis-of-baumgartners_15.html Mechanical analysis of Baumgartner's sky dive-part 2]

 

== WAVES AND MODERN PHYSICS ==





*[[Waves and Modern Physics]] 

== ELECTRICITY AND MAGNETISM ==
*[[Electricity and Magnetism]] 






== 210 Electromechanics ==
*[[Electromechanics]]

== SECONDARY 5 PHYSICS ==
*[[Secondary 5 Physics]]

== REMEDIAL ACTIVITIES FOR SECONDARY 4 ENVIRONMENTAL SCIENCE AND TECHNOLOGY ==
*[[Secondary 4 Physical Science]]

== KEVIN LENTON'S MECHANICS MODULES ==

== KRESHNIK ANGONI'S LECTURES ==

* [http://gauss.vaniercollege.qc.ca/~physics/KRESHNIK_LECTURES/NYA Mechanics (SN2)] 
* [http://gauss.vaniercollege.qc.ca/~physics/KRESHNIK_LECTURES/Electricity_Magnetism Electricity & Magnetism (SN2)] 
* [http://gauss.vaniercollege.qc.ca/~physics/KRESHNIK_LECTURES/NYC Waves & Modern Physics (SN3)] 
 

== LABS: USEFUL MATERIAL==

* [http://www.lon-capa.org/~mmp/applist/sigfig/sig.htm Significant Figures] 

* [http://www.learnerstv.com/animation/animation.php?ani=94&cat=physics Reading a Micrometer Scale] 

* [[Uncertainties in Measurement]]
:''by Kreshnik Angoni''


* [[Measurement and Data Analysis]]
:''by Kreshnik Angoni''

* [[Preparation for Labs]]
:''by Helena Dedic''


 

==ADDITIONAL RESOURCES==
* [[The Exponential Function and Its Applications in Science]]
*:''by Don Hetherington''

* [http://theengineerspulse.blogspot.com/p/for-physics-students.html Physics articles organized by course subject]
*:''by Stephen Cohen''

* [[Study Skills]]

* [https://www.youtube.com/channel/UCpVm6r2eaxwTcSznVPm51AA/playlists Videos by Learning Commons on Various Topics like referencing and use of Office365]

===Career-Related Articles===
* [[Things I wish I knew before my first job]]
*:''by Scott Redmond''

* [[Choosing the Right Career Path]]
*:''by Scott Redmond''

==PHYSICS '''''FUN'''''==


*[[A Light in the Dark]]
 


== FOR TEACHERS ==

* [http://gauss.vaniercollege.qc.ca/twiki Teacher WIKI]

Main Page

2026-02-13T15:26:24Z

Fuchs: /* KRESHNIK ANGONI'S LECTURES */

<big>'''Vanier College Physics Wiki'''</big>

Consult the [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.

== Getting started==
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]

==IMPORTANT DOCUMENTS==
Find your textbook, study guides and lab skills handbook here:
*[[STUDY DOCS]]



== MECHANICS ==
=== Introduction ===
* [http://stefan.bracher.info/files/physics/mechanics/mechanics_overview.pdf Mechanics Concept Overview]
* [http://stefan.bracher.info/files/physics/Formulas_and_Constants_for_College_Physics.pdf Stefan's Formulas for College Physics]
* [https://www.youtube.com/playlist?list=PLpDR89URs0h-zf-cHLTBNHUXOPYIEpWAg Stefan's Youtube Playlist for Mechanics]

=== Math review ===
==== Theory ====
* [http://stefan.bracher.info/files/physics/mechanics/Math_Review.pdf Stefan's Lecture Note on Math Review]

=== Measurement, Uncertainty, and Units ===
==== Videos ====
* [https://youtu.be/Kfy_Sd3jSCk Video: Introduction to uncertainties]
* [https://youtu.be/9YriBMqMx7c Video: Estimating the uncertainty of a measurement - Example: the length of a cat]
* [https://youtu.be/gHLzzzDohdE Video: Using the Min-Max Method to calculate the uncertainty of a measurement - Example: the length of a cat]
* [https://youtu.be/2ld3uFfRVt0 Video: Using the Average and Standard Deviation to calculate the uncertainty of a measurement - Example: the length of a cat]
* [https://youtu.be/e-Eb2wdZ-Qk Video: Accurate vs. Precise]
* [https://youtu.be/wyyBV3jnnZM?si=A8n01mY1oy_ffZ4W Video: An simple fix to improve the precision of a measurement]
* [https://youtu.be/7Q-zuT9cbeo Video: Calculations with uncertainty - Simple cases]
* [https://youtu.be/Lrkd6yHjTRI Video: Calculations with uncertainty - Complicated cases]
* [https://youtu.be/dumXDlANJA8 Video: Unit Conversion with dimensional analysis]
* [https://youtu.be/CLPjNelMLIs Video: Unit Conversion example: km/h to m/s]
* [https://youtu.be/7Vv7ExV87MU Video: SI-Prefixes]

==== Theory ====
* [http://gauss.vaniercollege.qc.ca/pwiki/index.php/Measurement_and_Data_Analysis Measurement and Data Analysis]
* [http://gauss.vaniercollege.qc.ca/pwiki/index.php/Uncertainties_in_Measurement Uncertainties in Measurement]
* [http://stefan.bracher.info/files/physics/mechanics/measurement_and_uncertainty.pdf Stefan's Lecture Note on Measurement and Uncertainty]

==== Book References ====
* [https://cnx.org/contents/1Q9uMg_a@13.38:bG-_rWXy@10/Introduction OpenStax University Physics Volume 1: Chapter 1.1-1.4]
* [https://cnx.org/contents/Ax2o07Ul@17.3:EC6WBNqn@13/1-2-Physical-Quantities-and-Units OpenStax College Physics: Chapter 1.2-1.3]

=== Vectors ===
==== Videos ====
* [https://youtu.be/jG6-AIGLOyM Video: Introduction to Vectors]
* [https://youtu.be/pDPOcpsdOXs Video: Drawing Vectors]
* [https://youtu.be/v2Cd4C7JXPY Video: Find the direction and the components of a vector]
* [https://youtu.be/OrryaQqcvk8 Video: Adding Vectors Graphically : Head to Tail Method]

==== Simulation ====
* [https://phet.colorado.edu/en/simulations/vector-addition Phet: Vector Addition]

==== Theory ====
* [[Vectors]]
* [http://stefan.bracher.info/files/physics/mechanics/Vectors.pdf Stefan's Lecture Note on Vectors]

==== Book References ====
* [https://cnx.org/contents/1Q9uMg_a@13.38:CEzSxrSw@8/Introduction Openstax University Physics Volume 1 - Chapter 2:Vectors]
* [https://cnx.org/contents/Ax2o07Ul@17.3:S9i77L2i@12/3-2-Vector-Addition-and-Subtraction-Graphical-Methods OpenStax College Physics - Chapter 3.2: Vector Addition and Subtraction: Graphical Methods]

=== Kinematics ===
*[[Basic Concepts]]

=====1 D Motion=====

====== Videos ======
* [https://youtu.be/g4s1j9nCyi4 Video: Introduction to Position-Time graphs]
* [https://youtu.be/YXrLMZb5uBA Video: Introduction to Velocity-Time graphs]
* [https://youtu.be/wArPnyyZCFg Video: Drawing the Position-Time graph from the Velocity-Time Graph]
* [https://youtu.be/wyZZn6sri5U Video: Kinematics Definitions, displacement, distance traveled, velocity and speed.]
* [http://stefan.bracher.info/files/physics/kinematics_formulas.htm Videos: Formulas for motion with constant acceleration]

* [https://youtu.be/-8eGB1WH0jw Video: Example - v-t, a-t and s-t graphs]
* [https://youtu.be/dKe0XFzSc6g Video: Example - Free-Fall]
* [https://youtu.be/q-TDxttAtLk Video: Example - Throwing an object in the air : Part 1]
* [https://youtu.be/nE5ePfnAyk8 Video: Example - Throwing an object in the air : Part 2]

* [https://youtu.be/22N1kAFx0L8 Video: Catch-up problems]

====== Theory ======
*[[Motion Along a Straight Line: Graphical Representation]] 
*[[Equations of Motion]]
* [[Free Fall]]

====== Simulation and practice ======
* [https://phet.colorado.edu/en/simulation/legacy/moving-man Simulation: Graphs]
* [https://www.geogebra.org/m/pdNj3DgD Geogebra: Create x-t and a-t graphs for various v-t graphs]
* [https://www.mathcelebrity.com/kinematic.php MathCelebrity: Kinematics Equations Calculator]

====== Book References ======
* [https://openstax.org/books/university-physics-volume-1/pages/3-introduction OpenStax University Physics Volume 1 - Chapter 3: Motion Along a Straight Line]
* [https://openstax.org/books/college-physics/pages/2-introduction-to-one-dimensional-kinematics OpenStax College Physics - Chapter 2: Introduction to One-Dimensional Kinematics]

=====2 D Motion=====
====== Videos ======
* [https://youtu.be/myHJ6_WS5OM Video: Introduction to 2D Kinematics]
* [https://youtu.be/_KyWgMUqP7k Video: Constant acceleration in 2D Kinematics]
* [https://youtu.be/tx8RMmVfy_E Video: Introduction to Projectile Motion]
* [https://youtu.be/x66EJxWhk8U Video: Projectile Motion Example - Angle and target location unknown]
* [https://youtu.be/vgUlurfyW0c Video: Projectile Motion Example - Maximal height and time to maximal height unknown]
* [https://youtu.be/qIi8-9rpRzU Video: Projectile Motion - Range and trajectory]
* [https://youtu.be/kwZ6_DAFFfE Video: Uniform Circular Motion - Centripetal Acceleration]

====== Theory ======
* [[Introduction to 2 D Motion]]
* [[Circular Motion]]
* [[Projectile Motion]]

====== Book References ======
* [https://openstax.org/books/university-physics-volume-1/pages/4-introduction OpenStax University Physics Volume 1 - Chapter 4: Motion in Two and Three Dimensions]
* [https://openstax.org/books/college-physics/pages/3-introduction-to-two-dimensional-kinematics OpenStax College Physics - Chapter 3: Introduction to Two-Dimensional Kinematics]

=====Rotational Kinematics=====
====== Videos ======
* [https://youtu.be/ZMZaO5mQLlE Video: Rotational Motion]
* [https://youtu.be/mwVww1NhIYk Video: Equations for constant angular acceleration]
* [https://youtu.be/3C4QfnlIQgM Video: Units of rotational motion (rpm)]
* [https://youtu.be/Nyv0SLEU2Aw Video: Rotational Kinematics Example]

====== Theory ======
* [[Rotational Motion]]


====== Book References ======
* [https://openstax.org/books/university-physics-volume-1/pages/10-introduction OpenStax University Physics Volume 1 - Chapter 10.1-10.3: Fixed-Axis Rotation]
* [https://openstax.org/books/college-physics/pages/10-introduction-to-rotational-motion-and-angular-momentum OpenStax College Physics - Chapter 10.1-10.2: Rotational Motion]

=== Dynamics ===
==== Videos ====
* [https://youtu.be/AUSXcozE_A0 Video: Introduction to Newton's Laws of Motion]
* [https://youtu.be/WzvhuQ5RWJE Video: Newton's 2nd Law of Motion]
* [https://youtu.be/cP0Bb3WXJ_k Video: Newton's 3rd Law of Motion]
* [https://youtu.be/dzdDzzRZm9U Video: Free Body Diagrams]
* [https://youtu.be/TLtGWls5F_I Video: Normal Forces Part 1]
* [https://youtu.be/JTeVBfUBdDs Video: Normal Forces Part 2]
* [https://youtu.be/t2RjGcvNSas Video: Tension Force]
* [https://youtu.be/dPSOs9lw90I Video: Simple Newton's Laws Problem Example]
* [https://youtu.be/ofeT2En6nz0 Video: Statics - Box on Surface]
* [https://youtu.be/R6ltYEMHuwc Video: Simple Dynamics Example]
* [https://youtu.be/pWsab45Httg Video: Two-body dynamics problem]
* [https://youtu.be/Y4FLaOTmklQ Video: Two boxes pushed along a surface]
* [https://youtu.be/JwEDFRDA5dc Video: Torque Shortcuts]
* [https://youtu.be/DMy6ree2sUA Video: Introduction to Rotational Equilibrium]
* [https://youtu.be/K1SxSdflCDA Video: Rotational and Translational Equilibrium - Beam with hanging mass]
* [https://youtu.be/XoAYWaDfs40 Video: Ladder leaning on the wall]
* [https://youtu.be/yC47CbcoWOE Video: Neil deGrasse Tyson: Einstein vs Newton - Who Was Right?]
* [https://youtu.be/lFgdmjmSxk0 Video: Newton's Universal Law of Gravity: Introduction]
* [https://youtu.be/xJqJ_UvBKiY Video: Newton's Universal Law of Gravity: Calculating the mass of the earth]
* [https://youtu.be/a-E28IqPVw8 Video: Newton's Universal Law of Gravity: Calculating the time it takes the moon to go around the earth]

==== Theory ====
*[[What is Dynamics?]]




*[[Inertia|The Concept of Inertia]] 
*[[Newton's Laws|Newton's Laws of Motion]] 
*[[Newton's Law of Universal Gravitation]] 
* [[Friction]]
*[[Dynamics of Circular Motion]] 
*[[Static and Dynamic Equilibrium]] 
*[[Torque]]


==== Book References ====
* [https://openstax.org/books/university-physics-volume-1/pages/5-introduction OpenStax University Physics Chapter 5: Newton's Laws of Motion]
* [https://openstax.org/books/university-physics-volume-1/pages/6-introduction OpenStax University Physics Chapter 6: Applications of Newton's Laws]
* [https://openstax.org/books/university-physics-volume-1/pages/10-6-torque OpenStax University Physics Chapter 10.6: Torque]
* [https://openstax.org/books/university-physics-volume-1/pages/10-7-newtons-second-law-for-rotation OpenStax University Physics Chapter 10.7: Newton's second law for rotation]

==== Simulations ====
* [https://phet.colorado.edu/en/simulation/forces-and-motion-basics Phet: Forces and Motion: Basics]
* [https://phet.colorado.edu/en/simulation/legacy/ramp-forces-and-motion Phet: Forces and Motion]
* [https://phet.colorado.edu/en/simulation/legacy/forces-and-motion Phet: Forces and Motion]
* [https://phet.colorado.edu/en/simulation/legacy/lunar-lander Phet: Lunar Lander]

=== Laws of Conservation ===
==== Videos - Basics of Conservation Laws ====
* [https://energy.ccdmd.qc.ca/videos/introduction-to-laws-of-conservation/ Video: Introduction to Laws of Conservation at CCDMD]
* [https://youtu.be/oDNAqnKhjZA Video: Introduction to Laws of Conservation (Conservation of Energy) by Stefan]

==== Videos - Energy ====
===== Videos - Conservation of Energy =====
* [https://energy.ccdmd.qc.ca/videos/introduction-to-conservation-of-energy/ Video: Introduction to Conservation of Energy at CCDMD]
* [https://energy.ccdmd.qc.ca/videos/conservation-of-energy-examples/ Video: Conservation of Energy Examples at CCDMD]

===== Videos - Energy in Mechanics =====
* [https://energy.ccdmd.qc.ca/videos/conservation-of-energy-in-mechanics/ CCDMD Video: Conservation of Energy in Mechanics]
* [https://youtu.be/a-4UISMSVpE Video: Conservation of Energy in Mechanics by Stefan]
* [https://energy.ccdmd.qc.ca/videos/conservation-of-energy-in-mechanics-exercise/ CCDMD Video: Conservation of Energy in Mechanics – Exercise]

===== Videos - Mechanical Work and Power =====
* [https://energy.ccdmd.qc.ca/videos/change-of-energy-through-mechanical-work/ CCDMD Video: Change of energy through mechanical work]
* [https://youtu.be/BEyZ60DHLnE Video: Mechanical Work by Stefan]
* [https://energy.ccdmd.qc.ca/videos/calculating-work-exercises/ CCDMD Video: Calculating work – Exercises]
* [https://energy.ccdmd.qc.ca/videos/introduction-to-power/ CCDMD Video: Introduction to Power]
* [https://energy.ccdmd.qc.ca/videos/power-exercise/ CCDMD Video: Power - Exercise]

===== Videos - Mechanical Energy =====
* [https://energy.ccdmd.qc.ca/videos/forms-of-energy-in-mechanics-discovery-of-kinetic-energy/ CCDMD Video: Forms of Energy in Mechanics: Discovery of Kinetic Energy]
* [https://energy.ccdmd.qc.ca/videos/forms-of-energy-in-mechanics-gravitational-potential-energy/ CCDMD Video: Forms of Energy in Mechanics: Gravitational Potential Energy]
* [https://energy.ccdmd.qc.ca/videos/forms-of-energy-in-mechanics-elastic-potential-energy/ CCDMD Video: Forms of Energy in Mechanics: Elastic Potential Energy]
* [https://youtu.be/y265HF0I1kg Video: Work required to lift an object (Discovery of Potential Energy) by Stefan]
* [https://youtu.be/a5qhsUWiZjw Video: Work required to accelerate an object to velocity v (Discovery of Kinetic Energy) by Stefan]
* [https://youtu.be/1XwxKKcn0ks Video: Conservative Forces and Potential Energy by Stefan]
* [https://youtu.be/CiSmPI4eHp8 Video: The potential energy of a spring by Stefan]
* [https://youtu.be/Jk9mYVAGHGk Video: Energy Example: Two connected blocks and a spring]
* [https://youtu.be/tGjZTRMSFBo Video: Energy Example: Calculating the escape velocity]
* [https://youtu.be/4HMXr7ExmBg Video: Pendulum Lab with Photogates - Conservation of Energy - Instructions]

===== Videos - Links to other courses (Chemistry, Thermodynamics, Applied Science, Engineering) =====
* [https://energy.ccdmd.qc.ca/videos/change-of-energy-through-heat/ CCDMD Video: Change of energy through heat]
* [https://energy.ccdmd.qc.ca/videos/thermal-energy/ CCDMD Video: Thermal Energy]
* [https://energy.ccdmd.qc.ca/videos/heat-machines/ CCDMD Video: Heat machines]
* [https://energy.ccdmd.qc.ca/videos/change-of-energy-through-heat-exercise/ CCDMD Video: Change of energy through heat – Exercise]
* [https://energy.ccdmd.qc.ca/videos/bernoullis-equation/ CCDMD Video: Bernoulli’s Equation (Fluid dynamics)]

===== Videos - Energy Review =====
* [https://energy.ccdmd.qc.ca/videos/popular-mistakes-with-conservation-of-energy/ CCDMD Video: Popular mistakes with conservation of energy]

==== Videos - Momentum ====
* [https://youtu.be/dNOthHSV0RM Video: Introduction to Linear Momentum]
* [https://youtu.be/I_RNxh8Eb-s Video: Conservation of Linear Momentum - Inelastic Collision]
* [https://youtu.be/ym2c6k09YY4 Video: Conservation of Linear Momentum - Example: 1D Inelastic Collision]
* [https://youtu.be/Fq7CasNQ_m0 Video: Conservation of Linear Momentum - Elastic Collision]
* [https://youtu.be/TArgOS55--I Video: Conservation of Linear Momentum - 2D Collision Example]
* [https://youtu.be/tXeQKIlxQEk Video: Conservation of Linear Momentum - Explosions]
* [https://youtu.be/zsMvyDSDPtI Video: Conservation of Linear Momentum - Rocket Equation (this is Rocket Science!)]
* [https://youtu.be/2FmyyHR47Xo Video: Conservation of Linear Momentum - Linear Momentum and Newton]
* [https://youtu.be/mqU9XBZ-jnw Video: Conservation of Angular Momentum - Introduction]
* [https://youtu.be/ULAar-EtJQI Video: Conservation of Angular Momentum - Changing the rotational inertia]
* [https://youtu.be/_RVe_ii-YJ4 Video: Conservation of Angular Momentum - A rotating platform]
* [https://www.youtube.com/watch?v=iaauRiRX4do Video: Conservation of Angular Momentum]

==== Theory ====
* [[Work and Energy]]

* [[Potential Energy]]

* [[Conservative and Non-Conservative Forces]]

* [[Conservation of Energy]]

* [[Rotational Kinetic Energy and Moment Of Inertia]]

* [[Conservation of Momentum|Conservation of Linear Momentum]] 

==== Book References ====
* [https://energy.ccdmd.qc.ca/glossary/ CCDMD: Glossary]
* [https://openstax.org/books/university-physics-volume-1/pages/7-introduction Openstax University Physics Volume 1: Chapter 7 (Work and Kinetic Energy)]
* [https://openstax.org/books/university-physics-volume-1/pages/8-introduction Openstax University Physics Volume 1: Chapter 8 (Potential Energy and Conservation of Energy)]
* [https://openstax.org/books/university-physics-volume-1/pages/9-introduction Openstax University Physics Volume 1: Chapter 9 (Linear Momentum and Collisions)]
* [https://openstax.org/books/university-physics-volume-1/pages/11-introduction Openstax University Physics Volume 1: Chapter 11 (Angular Momentum)]

=== Summary ===
* [https://youtu.be/3RnIH4_3E1U Video: Summary of Mechanics]

== STEFAN BRACHER'S LECTURES ==
*[http://stefan.bracher.info/physics_mechanics.php Stefan's Lecture notes for Mechanics]
 
== Interesting Articles on Mechanics ==

*[[My Daughter,the Physicist]]
:''by Stephen Cohen''

=====Felix Baumgartner's Sky Dive=====

[http://theengineerspulse.blogspot.ca/2012/10/mechanical-analysis-of-baumgartners.html Mechanical analysis of Baumgartner's sky dive]
 

[http://theengineerspulse.blogspot.ca/2012/10/mechanical-analysis-of-baumgartners_15.html Mechanical analysis of Baumgartner's sky dive-part 2]

 

== WAVES AND MODERN PHYSICS ==





*[[Waves and Modern Physics]] 

== ELECTRICITY AND MAGNETISM ==
*[[Electricity and Magnetism]] 






== 210 Electromechanics ==
*[[Electromechanics]]

== SECONDARY 5 PHYSICS ==
*[[Secondary 5 Physics]]

== REMEDIAL ACTIVITIES FOR SECONDARY 4 ENVIRONMENTAL SCIENCE AND TECHNOLOGY ==
*[[Secondary 4 Physical Science]]

== KEVIN LENTON'S MECHANICS MODULES ==

== KRESHNIK ANGONI'S LECTURES ==

* [http://gauss.vaniercollege.qc.ca/~physics/KRESHNIK_LECTURES/NYA Mechanics (SN2)] 
* [http://gauss.vaniercollege.qc.ca/~physics/KRESHNIK_LECTURES/Electricity&Magnetism Electricity & Magnetism (SN2)] 
* [http://gauss.vaniercollege.qc.ca/~physics/KRESHNIK_LECTURES/NYC Waves & Modern Physics (SN3)] 
 

== LABS: USEFUL MATERIAL==

* [http://www.lon-capa.org/~mmp/applist/sigfig/sig.htm Significant Figures] 

* [http://www.learnerstv.com/animation/animation.php?ani=94&cat=physics Reading a Micrometer Scale] 

* [[Uncertainties in Measurement]]
:''by Kreshnik Angoni''


* [[Measurement and Data Analysis]]
:''by Kreshnik Angoni''

* [[Preparation for Labs]]
:''by Helena Dedic''


 

==ADDITIONAL RESOURCES==
* [[The Exponential Function and Its Applications in Science]]
*:''by Don Hetherington''

* [http://theengineerspulse.blogspot.com/p/for-physics-students.html Physics articles organized by course subject]
*:''by Stephen Cohen''

* [[Study Skills]]

* [https://www.youtube.com/channel/UCpVm6r2eaxwTcSznVPm51AA/playlists Videos by Learning Commons on Various Topics like referencing and use of Office365]

===Career-Related Articles===
* [[Things I wish I knew before my first job]]
*:''by Scott Redmond''

* [[Choosing the Right Career Path]]
*:''by Scott Redmond''

==PHYSICS '''''FUN'''''==


*[[A Light in the Dark]]
 


== FOR TEACHERS ==

* [http://gauss.vaniercollege.qc.ca/twiki Teacher WIKI]

The Electric Field

2025-01-31T16:15:43Z

Fuchs:

Back to [[Electricity_and_Magnetism]]

= Textbook =
[https://openstax.org/books/university-physics-volume-2/pages/5-4-electric-field University Physics Volume 2: Chapter 5.4]

= Electric Fields Videos =

= Theory =
== Electric Field ==
The electric field acts as a shortcut for calculating the electric force <math> \vec{F} </math> on a test charge <math> q </math>, similar to how the gravitational field <math> g </math> simplifies calculations for gravitational force. Instead of recalculating the force based on Coulomb's Law (and adding the forces of multiple source charges), we can use the electric field, where:

<math> \vec{F} = q_t \cdot \vec{E} </math>

In the same way that <math> \vec{g} </math> gives the gravitational force per kilogram, <math> \vec{E} </math> gives the electric force per coulomb.

=== The Electric Field of a Charged Particle at rest (Point Charge) ===

The electric field <math> \vec{E} </math> caused by a point (source) charge <math> Q_s </math> at a distance <math> r </math> from the position is given by:

<math> \vec{E} = k_e \frac{Q_s}{r^2} \hat{r} </math>

where:
* <math> k_e </math> is the electrostatic constant, approximately <math> 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 </math>.
* <math> Q_s </math> is the point charge creating the electric field (the source charge).
* <math> r </math> is the distance from the charge to the point where the field is being calculated.
* <math> \hat{r} </math> is a unit vector pointing from the charge to the point of interest.

Note that combined with <math> \vec{F} = q_t \cdot \vec{E} </math>, this simply gives you Coulomb's Law.

<youtube>qMnQQudvaE4</youtube>
<youtube>pB-Fjrs1m94</youtube>
 

== Electric Field Lines ==

'''Electric field lines''' visually represent the direction and strength of an electric field around charges. They point in the direction the electric force would have on a positive test charge.

* Direction: Field lines point '''away''' from positive charges and '''toward''' negative charges.
* Density: The closer the lines, the stronger the electric field in that area.

=== Rules for Drawing Electric Field Lines ===
* Lines start or end on charges, with more lines indicating a larger charge magnitude.
* Field lines never cross.
* They form continuous, smooth curves.

<youtube>pbrI1JEBAQU</youtube>
 

== Typical Problems with the Electric Field ==
<youtube>8GzJOKjp_jA</youtube>
 

== Other Videos ==
[https://youtu.be/WqvImbn9GG4 MIT Physics Demo -- Faraday's Cage] 
<youtube>M1XHjl_6HtM</youtube> 
<youtube>Zi4kXgDBFhw</youtube> 
 

= Simulations =
*[https://phet.colorado.edu/en/simulations/efield PhET Simulation: Electric Field of Dreams] 
*[https://phet.colorado.edu/en/simulations/charges-and-fields PhET Simulation: Charges and Fields] 
*[https://phet.colorado.edu/en/simulations/electric-hockey PhET Simulation: Electric Field Hockey] 
*[https://phet.colorado.edu/en/simulations/radio-waves PhET Simulation: Radio Waves & Electromagnetic Fields] 
*[https://phet.colorado.edu/en/simulations/microwaves PhET Simulation: Microwaves] 

= Other Links =

[https://iwant2study.org/lookangejss/05electricitynmagnetism_11efield/ejss_model_electricfieldwee/electricfieldwee_Simulation.xhtml Electric Field vectors] 

[https://www.falstad.com/vector3de/ The Electric Field-3D]
 

[http://ffden-2.phys.uaf.edu/212_fall2003.web.dir/kristina_smith/description.html Lightning applet] 

 
Back to [[Electricity_and_Magnetism]]
 
Next: [[Electric Potential]]

Electricity and Magnetism

2024-08-26T02:04:48Z

Fuchs:

*[[Electrostatics]]

*[[The Electric Field]]

*[[Capacitors]] 

*[[Magnetic Fields]]

*[[Notes on DC Circuits]]


*[[The role of a battery in a circuit]]



== NUZHAT JILANI'S LECTURES ==

* [http://gauss.vaniercollege.qc.ca/~physics/NJ_LECTURES/NYB NYB]

Technical document sample

2010-02-26T19:34:04Z

Fuchs:

== Project 0 ==

'''Introduction'''

Gaussian elimination is an algorithm used to solve system of equations. In the physical world, this technique can be used it to balance chemical equations, analyze electrical networks, and study the flow of traffic at a particular intersection.

== Balancing Chemical Equations ==

An application of Gaussian elimination comes in the form of balancing equations which represent a chemical reaction. By definition, a chemical reactions occurs when a number of molecules combine to form new molecules.

In general, balancing a chemical reaction using matrices requires us to first, designate variables for the reactants and products. Secondly, we then equate the various elements from the left hand of the equation to the right hand components; this will generate a set of equations. To solve this set of equations, we then need to convert it into a homogeneous system, and represent it as a coefficient matrix. The rows of the matrix represent the quantity of each element in the unbalanced equations, whereas the columns represent the variables used to designate the number of molecules that are required by each compound in the final balanced equation.

To determine the balanced form of the equation, Gaussian elimination will be applied onto the matrix until a reduced row echelon form has been attained. Generally, a parameter will be required. The value of this parameter will be the smallest number which forces all other values to be positive and whole, since all reactions require integral molecules as opposed to fractions of them to complete the reaction.

== Example ==

Photosynthesis is a process which harnesses the sun's energy, in the form of light, to convert carbon dioxide into sugar. Below is the chemical reaction for photosynthesis, which combines carbon dioxide with water to produce glucose and oxygen.

<math>CO_2+H_20\rightarrow C_6H_{12}O_6 + O_2</math>

Balance this chemical equation.

== Solution ==

The first step in balancing the reaction, is to designate the variables <math>\it{w}, \it{x}, \it{y}, \it{z}\in N </math> such that

<math>\it{w}CO_2+\it{x}H_20\rightarrow \it{y}C_6H_{12}O_6 + \it{z}O_2</math>

We now equate the number of carbon, hydrogen, and oxygen atoms to form the following set of equations:

<math>

\begin{align}
w &= 6y \\
2w + x &= 6y +2z \\
2x &= 12y\\
\end{align}</math>

To simplify the process of obtaining the solution, the above set of equations has been converted into a homogeneous system:

<math>

\begin{align}
w -6y &= 0 \\
2w + x -6y - 2z&= 0 \\
2x -12y&= 0\\
\end{align}</math>

'''Remark''': In both systems (preliminary and homogeneous) each line (equation) represents one of the elements in the reaction.

To solve the homogeneous system, we apply Gaussian Elimination onto the system until a reduced row echelon form has been attained.

<math>

\begin{pmatrix}
1 & 0 & -6 & 0 &0\\
2 & 1 & -6 & -2 &0\\
0 & 2 &-12 & 0 &0
\end{pmatrix}
</math>

What follows is a series of row operations that take the above matrix to RREF.
<math>

\begin{pmatrix}
1 & 0 & -6 & 0 &0\\
2 & 1 & -6 & -2 &0\\
0 & 2 &-12 & 0 &0
\end{pmatrix}
</math>

<math>
-2R_1+R_2\rightarrow R_2

\begin{pmatrix}
1 & 0 & -6 & 0 &0\\
0 & 1 & 6 & -2 &0\\
0 & 2 &-12 & 0 &0
\end{pmatrix}
</math>

<math>

-2R_2+R_3\rightarrow R_3

\begin{pmatrix}
1 & 0 & -6 & 0 &0\\
0 & 1 & 6 & -2 &0\\
0 & 0 &-24 & 4 &0
\end{pmatrix}
</math>

<math>

\frac{-1}{24}R_3\rightarrow R_3

\begin{pmatrix}
1 & 0 & -6 & 0 &0\\
0 & 1 & 6 & -2 &0\\
0 & 0 &1 & \frac{-1}{6} &0
\end{pmatrix}
</math>

<math>

-6R_3 + R_2\rightarrow R_2

\begin{pmatrix}
1 & 0 & -6 & 0 &0\\
0 & 1 & 0 & -1 &0\\
0 & 0 &1 & \frac{-1}{6} &0
\end{pmatrix}
</math>

<math>

6R_3 + R_1\rightarrow R_1

\begin{pmatrix}
1 & 0 & 0 & -1 &0\\
0 & 1 & 0 & -1 &0\\
0 & 0 &1 & \frac{-1}{6} &0
\end{pmatrix}
</math>

Observe that we have four variables, but only three equations. As a result, we need to set a parameter. So from our final matrix, we see that

<math>
\begin{align}
w - z &=0\\
x - z &=0\\
y -\frac{1}{6}z&=0\\

\end{align}
</math>
Which is equivalent to

<math>
\begin{align}
w &=z\\
x &=z\\
y &=\frac{1}{6}z\\

\end{align}
</math>

If we let <math> z=t</math>, then
<math>
\begin{align}
w &=t\\
x &=t\\
y &=\frac{1}{6}t\\
z &=t\\

\end{align}
</math>

Smallest value for which <math>z</math> can be set to so that we have postive and whole numbers for the other variables is <math> 6</math>. So <math> w=6, x=6, y=1</math>, and <math>z=6</math>. The balanced equation is therefore:

<math>
6CO_2 + 6H_2O \rightarrow C_6H_{12}O_6+6O_2
</math>

Vtest

2010-02-26T19:21:00Z

Fuchs:

===Videoclips===

See how the horizontal range of a projectile depends on the initial angle of incidence. The initial velocity is the same in each case:
:::::<youtube>N0H-rv9XFHk</youtube>

Parabolic motion versus vertical free fall:
:::::<youtube>z24_ihikEqQ</youtube>

Projectile Motion, velocity vector:
:::::<youtube>ZBfy-MNgtoY</youtube>

The monkey and the gun. The monkey falls downward at the same rate as the bullet. The acceleration due to gravity is the same for both, even though the bullet is fired with a higher initial velocity.
:::::<youtube>cxvsHNRXLjw</youtube>

''Kreshnik Angoni''

Using graphs during measurements is very important because one can get straight away initial information about high error measurements data and simply avoid them from further treatments. To do this, one must be aware about the possible results.

===Estimation of Uncertainties in Measurements Results===
====First Step====
Suppose we want to verify if the period of oscillations is constant or changes in time.

[[image:Graph1_Uncertainty.PNG|top]] 
We take several period measurements in different moments and have values 1.99s, 2.01s, 1.89s, 2.05s 1.96s, 1.99s, 2.68s, 1.97s, 2.03s, 1.95s; To have a first information we put these data in a graph. From this graph we have the information that it is very likely that
the T might be constant in time (~2s). The seventh measure seems too far from the other results and this might be due to an abnormal circumstance during measure. To eliminate any doubt, we neglect (cancel) this value from the following error analysis. We have enough other data to work with. Our remaining data are: 1.99s, 2.01s, 1.89s, 2.05s 1.96s, 1.99s, 1.97s, 2.03s, 1.95s;. If necessary, one has to gather new data. Note: Consider five measurements as a minimum number of data for estimating a parameter (repeat 5 times).

====Second Step====
As no-one knows the real value of period T, we try to find an estimation for this value by using the average of data measurements
<math>\bar{T}= \frac{1}{2}\sum_{i=1}^nT_i = \frac{1}{2}\sum_{i=1}^9T_i = \frac{1}{2}[1.99+2.01+1.89+2.05+1.96+1.99+1.97+2.03+1.95] = 1.982 s</math>

====Third Step====

To get better information about the measurement and its results we need to know the measurements spread. A first way to estimate the spread is by use of “average distance” of data from the average one. So we get

<math>\Delta T = \frac{1}{2}\sum_{i=1}^n \left |T_i - \bar{T}\right | = \frac{1}{2}\sum_{i=1}^9 \left |T_i - 1.982\right | = 0.035 s</math>

Now we can say that the real value of period is inside the interval (1.982 +/- 0.035)s or it is between T_{max} = 2.017s and T_{min} =1.947s with average value 1.982s. The relative uncertainty of these measurements is

<math>\varepsilon = \frac {\Delta T}{\bar{T}}*100% =\frac {0.035}{1.982}*100% = 1.81% </math>.

As this value is < 5% we can affirm that the period is a constant in this experiment.
'''Note:''' We will accept that our measurement method is enough precise if the relative uncertainty of measurements for the same value of a physical quantity or a physical constant is <math>\varepsilon\le 5%</math> .

A second and statistically better way to estimate the spread is by use of “standard deviation” of data 
<math>\sigma T = \sqrt{\frac{\sum_{i=1}^n \left (T_i - \bar{T}\right )^2}{n-1}} = \sqrt{\frac{\sum_{i=1}^9 \left (T_i - 1.982\right )^2}{8}} = 0.047 s</math> 
Using standard deviation we find the relative uncertainty of measurements as
<math>\frac{\sigma T}{T} *100% = \frac{0.047}{1.982} * 100% = 2.37%</math>

This value is < 5%, too. If the relative uncertainty is > 5%, we may proceed by: 
a) Cancelling the data “shifted the most from the average value” 
b) Increasing the number of data by repeating more times the measurement 
c) Improving the measurement procedure 

===Estimation of Uncertainties for Calculated Quantities (Uncertainty propagation)===
====Max-Min method====
Often, the measurements data of some physical quantities are used to calculate, by the way of a known expression, the value for another physical quantity. 
'''Rule No1:''' 
Calculate the average of the quantity in interest by average values of the measured quantities. Example: The circular frequency of oscillations is calculated as <math>\omega = \frac{2\pi}{T}</math> . By using the upper results for period measurement we can calculate <math>\omega_{AV} =\frac{2\pi}{\bar T} = \frac{2 * 3.14}{1.982} = 3.168 rad/s</math>.
What is the absolute uncertainty for this estimation of ω? 
 '''Rule No2:''' 
We have to define carefully the effect (increase or decrease) of each primary quantity over that in interest and use the minimum and maximum known values of primary quantities.
Note: When calculating an extreme value of the quantity in interest, one selects the combination of maximum or minimum values of primary quantities in dependence on the math function. Example:
<math>\omega_{MAX} = \frac{2\pi}{T_{MIN}} = \frac{2*3.14}{T - \Delta T} =\frac {6.28}{1.947} = 3.22rad/sec</math>
and
<math>\omega_{MIN} = \frac{2\pi}{T_{MAX}} = \frac{2*3.14}{T + \Delta T} =\frac {6.28}{2.019} = 3.11rad/sec</math>

Note that if the relation was z = x – y one would get <math>z_{MAX} = x_{MAX} - y_{MIN}</math> and <math>z_{MIN} = x_{MIN} - y_{MAX}</math>
Note. You may start calculations by finding first <math>z_{MAX}, z_{MIN}</math> and then calculate <math>z_{AV} = \frac {z_{MAX}+z_{MIN}}{2} </math> 
'''Rule No3:''' 
One calculates the absolute uncertainty as <math>\Delta z = \frac {z_{MAX}- z_{MIN}}{2} </math> 
Example: <math>\Delta \omega = \frac {\omega_{MAX}- \omega_{MIN}}{2} = \frac{3.22 - 3.11}{2} = 0.06 r/s. </math> 
'''Rule No4:''' 
One calculates the relative uncertainty of estimation for the calculated quantity as the ratio of 
What way must appear the result of our measurements?

The final answer about the upper example is:
The true value of <math>\omega</math> is inside the interval 3.11rad/s and 3.22rad/s.
The estimated average value is 3.17rad/sec
The relative uncertainty of the estimation is 1.89%

Note: Uncertainties of final results are normally quoted to the same number of digits after the decimal point as the average value; the result should then be rounded off appropriately. The use of scientific notation helps to prevent confusion about the number of significant figures. Example: If calculations generate, say A = 0.03456789 ± 0.00245678. This should be presented after being rounded off (one or two significant figure after decimal point ):
A = (3.5 ± 0.2) x 10-2 or A = (3.46 ± 0.25) x 10-2