## Rotational Dynamics

For linear motion, we used Newton's Laws of Motion and, in particular, Newton's Second Law of Motion,

F = m a and

The rotational equivalent of

F= mais

= I where (the lower case Greek letter "alpha") is the angular acceleration we have just seen and (the lower case Greek letter "tau") is the "torque" or "rotational force" we recently saw in our study of static equilibrium and I is the "moment of inertia" or the "rotational mass".

I = m r ^{2}That is, the rotational mass depends upon the

distributionof the mass. Here are a few sample values of this "rotational mass":If you

needa value for the rotational mass or the moment of inertia, you can always look it up. These are not things worth memorizing. However, you do need to know that and object with its mass far from the center has a greater moment of inertia than another object (of the same mass) with its mass near the center.

Masses close to the axis of rotation have a small rotational mass. This means they are easy to rotate.

Masses far from the axis of rotation have a large rotational mass. This means they are difficult to rotate.Click herefor anEXAMPLE.

Rotational KinematicsAngular MomentumReturn to ToC, Rotational Motion(c) 2002, Doug Davis; all rights reserved