Inertia of Weight

Inertia of Weight is the moment of inertia of the counterweight around its center of gravity.

The moment of inertia can be found by breaking the weight up into simple shapes, finding the moment of inertia for each one, and then combining them together using the parallel axis theorem. A list of formulas for the moment of inertia of different shapes can be found here. The Arm Example Calculations show how to do this for the arm. A similar procedure can be used for the weight.

Alternatly, using a 3D CAD software package is probably the easiest way to find the inertia of the weight.

In general, it is better to have a weight with a small inertia. However a larger inertia comes with a heavier weight. The easiest way to get around this is by having a weight that is able to pivot. If you do this you can set the inertia of the weight to a small number.

Mass of Weight

Mass of Weight is the mass of the counterweight.

In general, the projectile will go farther with a heavier counterweight.