Moments of Inertia Demo

Theory

Total Energy = Potential Energy at the top of the board = Translational Energy (m*v*v/2) + Rotational Energy (I*w*w/2). Since the hoop has an I value of M*R*R and the wooden disk is half that, the hoop will only have 3/4 of the velocity of the disk at a particular height. By the equation V2=V2o+2a(x-xo), the distance the hoop travels by a particular time will be the square root of 3/4 times the distance travelled by the disk.

Apparatus

The equipment needed for this demo is:

* A hoop and disk
* an inclined plane (board and prop)
* a meter stick
* a timing device

Procedure

Place the wheels at the top of the inclined plane, keeping them from touching. Let them roll down the plane and have a student time their trip to the bottom. Then let them roll down the plane and stop them when the disk reaches the bottom. The hoop should be sqrt(3/4)= (.866) of the way to the bottom.

Helpful Hints

(1) Try to line up the wheels so they roll down the plane relatively straight. Having one roll off to the side wastes time and looks bad.
(2) Don't prop the box on anything that will fall easily; when you stop the disk and hoop, the whole apparatus could topple.
(3) Don't waste time measuring angles or coefficients of friction if the calculations can all be done as ratios.