Game Development Reference
Figure 14.11. The annular cylinder used in Exercise 4.
Figure 14.12. The capsule used in Exercise 5.
in Figure 14.12. Let m be the total mass of the capsule and assume a uniform
density ρ . [ Hint. Combine the inertia tensors for a cylinder and two domes
in the appropriate way.]
Suppose that an object of mass m is hanging from a rope of negligible mass
that is wrapped around a cylindrical spool many times (see Figure 14.13). If
the cylinder has mass M and radius R , determine at what rate a the object
accelerates downward under the influence of gravity. Assume that the rope
does not slip as it unwinds from the spool. [ Hint. As gravity pulls on the ob-
ject, it creates a tension T in the rope that is counteracted by the cylinder, so