imported>Patrick at 16:05, 20 July 2011

2011-07-20T16:05:48Z

New page

''Helena Dedic''
 

''If you need to understand the concept of center of mass, please see the link below:'' 
[[Rotational Kinetic Energy and Moment Of Inertia|CENTER OF MASS]]
 

*A force causes a free object to move in a translational motion if it is applied at the centre of mass of the object or the line of force passes through the centre of mass. 
[[image:Helena_Torque_1.png|TOP]] 

*When a force is not applied at the centre of mass of a free object or when the line of force does not pass through the centre of mass then it causes this object to move in a complex way that involves both translation (i.e.: movement of the center of mass) as well as rotation (i.e.: movement around the center of mass.) 
[[image:Helena_Torque_2.png|TOP]] 

*OBSERVATIONS OF AN OBJECT:

'''a)''' When a force acts at the pivot or when a line of force passes through the pivot, 
the object does not begin to rotate.
[[image:Helena_Torque_3.png|TOP]] 

'''b)''' When a force acts at some distance from the pivot, the object begins to rotate.
[[image:Helena_Torque_4.png|TOP]] 

*Lever arm is a vector that points from the pivot to the point where the force acts. 
[[image:Helena_Torque_5.png|TOP]] 

*'''TORQUE''': '''A cause of a change of the angular velocity''' (e.g.: a rotating wheel stops or it begins to rotate faster.

The symbol for torque is <math>\vec{\tau}</math>.

*'''Magnitude and direction of the torque''': The magnitude of the torque depends on the magnitude of the lever arm, the magnitude of the force and the angle between these two vectors:

<math>\tau = \pm F r \sin{\theta}</math>

In special cases where the axis of rotation is given: The torque is '''positive''' when the torque causes the object to rotate in the '''counter-clockwise''' direction and '''negative''' when the torque causes the object to rotate in the '''clockwise''' direction. 

*In general the torque is a vector product of the lever arm and the force:

<math>\vec{\tau} = \vec{r} \times \vec{F}</math>
 
[[Exercises on Torque|EXERCISES ON TORQUE]] 

===Static Equilibrium Revisited===

*An object is in static equilibrium '''if and only if''' <math>\vec{\tau}_{net} = 0</math> and <math>\vec{F}_{net} = 0</math>, where the net torque is the sum of all torques and the net force is the sum of all forces acting on an object. 
*Static equilibrium '''problem solving strategy''': 
#Determine all forces acting on an object and draw an arrow for each force indicating:
#*A point where this force is applied
#*In which direction this force acts
#For each force:
#*Identify the magnitude and the direction of lever arm
#*Draw a diagram consisting of lever arm and force vectors and determine the angle between these two vectors
#*Determine the direction of the torque and then compute its magnitude.
#Substitute into the equation <math>\Sigma \tau = 0</math>
#Select the coordinate system
#Draw a free-body diagram
#Compute the components of the forces
#Substitute into the equations <math>\Sigma F_x = 0</math> and <math>\Sigma F_y = 0</math>
#Solve the system of three equations using the method of substitution
 
[[Exercises on Static Equilibrium|EXERCISES ON STATIC EQUILIBRIUM]]

Torque - Revision history

imported>Patrick at 16:05, 20 July 2011