(a) A circular hoop of mass m and radius r spins like a wheel while its center remains at rest. Its period (time required for one revolution) is T. Show that its kinetic energy equals 2π 2mr2/T2 . (b)...

(a) A circular hoop of mass m and radius r spins like a wheel while its center remains at rest. Its period (time required for one revolution) is T. Show that its kinetic energy equals 2π 2mr2/T2 . (b) If such a hoop rolls with its center moving at velocity v, its kinetic energy equals (1/2)mv2 , plus the amount of kinetic energy found in the first part of this problem. Show that a hoop rolls down an inclined plane with half the acceleration that a frictionless sliding block would have.