Kevin at 00:48, 8 May 2014

2014-05-08T00:48:25Z

New page

''Kreshnik Angoni and Kevin Lenton''
 
[http://gauss.vaniercollege.qc.ca/~physics/MechanicsModules/Module%20Worksheets/NYB/MagneticInduction/MagneticInduction.docx Worksheet.docx] 
[http://gauss.vaniercollege.qc.ca/~physics/MechanicsModules/Module%20Worksheets/NYB/MagneticInduction/MagneticInduction.pdf Worksheet.pdf] 

Other Resources: 
*Haliday & Resnick, Fundamentals of Physics 9.4-11
*[http://cnx.org/content/m42155/latest/?collection=col11406/1.7 Openstax]
* [http://fclass.vaniercollege.qc.ca/~angonik/FOV1-00042F8A/FOV1-0006425E/FOV1-0006425F/LECTURE_11.pdf?FCItemID=S00282F7E Printable version]
 

===The Moment of Inertia: the rotational equivalent of mass===
A definition of mass comes from Newton's second Law: the mass of an object defines how an object will accelerate given a certain linear net force. 
You could say the mass shows you how an object will move. We need an equivalent to describe how an object will ''rotate'', given a net torques. This equivalent is called the ''The Moment of Intertia'', given the symbol ''I''. 
The quantity ''I'' [Units:kg*m2] is called the moment of inertia of the body with respect to the rotation axis. You can tell from the units that the Moment of Inertia is always a mass times radius squared. The exact
numerical value of I depends on the way that the mass of the body is distributed spatially with respect to
a particular axis. A quick comparison of expression (22) with K = mv2/2 allows to figure out that, in a
rotational motion, I is playing the role of the mass for translational motion. So, we can derive that

The inertia moment is a measure of the resistance a body presents to the change of its rotational

status of motion or in other terms to its existing angular velocity. 

You can get a feel for the moment of inertia by trying to rotate a hammer. If you hold it by the wooden end, and try and spin it (the mass is further away from the pivot i.e. bigger moment of inertia ) it is much more difficult to spin
than when holding it by the metallic end (more of the mass is closer to the pivot, smaller r, therefore smaller inertia moment). 

- Straight from the definition (23) we may see that the same mass
located at a bigger distance from the axis produces bigger moment
of inertia. So, one may guess that, for the same mass, the inertia
moments versus the central axis of symmetry for a ring, a disk, and
a cylinder (figure 9) are different and Iring >Idisk >Icylinder.
 
The center of mass CM of the body is a physical concept that
helps a lot to find I-value for any position of rotation axis.

 

Figure 9

Module : Rotational Dynamics - Revision history

Kevin at 00:48, 8 May 2014