Rotational Work and Kinetic Energy

There are rotational equivalents to the rules of linear dynamics, and rotational equivalents to the linear quantities described by those rules.
Work done by a linear force is Work = force * distance; in the rotational world, work is done by a torque applied through some angle:
```
            work   =  (torque) * (angle) 
```
Translational kinetic energy is KE = 0.5 * mass * speed^2; in the rotational world, kinetic energy depends on the moment of inertia of a body, and its angular speed:
```
           rot KE  =  0.5 * (moment of inertia) * (angular speed)^2
```
If a body rolls down a hill, it must split the gravitational potential energy it loses into two pieces: a translational KE and a rotational KE. That means that it must have less translational energy than an object which just slides. So rolling objects move more slowly than sliding ones, all other things being equal.

Viewgraphs