A sphere or cylinder of mass M, radius R, and moment of inertia I rolls without slipping down a hill of height h, starting
from rest. As explained in Problem 9.P.38, if there is no slipping ω = vCM/R.
(a) In terms of the given variables (M, R, I, and h), what is vCM at the bottom of the hill?
(b) If the object is a thin hollow cylinder, what is vCM at the bottom of the hill?
(c) If the object is a uniform-density solid cylinder, what is vCM at the bottom of the hill?
(d) If the object is a uniform-density sphere, what is vCM at the bottom of the hill?
An interesting experiment that you can perform is to roll various objects down an inclined board and see how much time
each one takes to reach the bottom.