Some Important Numbers

The moment of inertia of the wooden dowel/silvered mass combination is 2.048*10^-3 Kg*m².

The distance to the center of mass, l, of the wooden dowel/silvered mass combination is 40.167 cm. (The wooden dowel is 45.72 cm long, though.)

The mass of the vehicle, M, includes all masses except the mass of the wooden dowel and silvered mass which constitute m, the mass of the pendulum.

The mass of the vehicle, no batteries, no mass on the pendulum, no circuit, is 805.13 grams.

The mass of the silvered mass used on the pendulum for demonstrations is 161.59 grams.

The batteries, in the battery holder, are 212.62 grams.

Therefore, since the acceleration tests were performed with the batteries and the silvered mass on the vehicle, the total mass of the vehicle during the accelerations tests was 1179.34 grams.

The rolling resistance of the vehicle, as tested for acceleration, is 1.226 Newtons.

The mass of the wooden dowel that may be used as the pendulum is 73.71 grams. Its length is 90.17 centimeters, so it is 0.8175 grams per centimeter.

The circuit board with all components will be from 28 to 43 grams.

In determining the moment of inertia of the silvered mass we assume that it is a sphere. Thus the equation for the moment of inertia is

.

Its diameter is 3.35 cm and its mass is 161.59 g.

In determining the moment of inertia of the wooden dowel it is assumed to be a slender rod--a near-valid assumption since it has only one degree of freedom. It's moment of inertia is

.

Its mass is 37.376 g (based on mass per centimeter given above) and its lenght is 45.72 cm.

Both of the inertias derived above are about the object's center of mass. In order to get the combined moment of inertia, the composite's center of mass must be determined. In order to do this an arbitrary point must be chosen as the reference. Using

the distance from the arbitrary point to the composite center of mass can be determined. r_c is the distance from the arbitrary point to the center of mass. In this case the arbitrary point was chosen to be the axis of rotation for the pendulum--not so terribly arbitrary.

 Once the composite center of mass is known the composite moment of inertia may be determined by first using

,

where is the moment of inertia of an object about its center of mass, for each mass and then simply adding the resulting moments together.