A) at What Rate Was It Rotating at the Base of the Hill?

1. A string is wrapped several times around the rim of a small hoop with a radius of 0.0800 m and a mass of 0.180 kg. If the free end of the string is held in place and the hoop is released from rest, calculate the angular speed of the rotating hoop after it has descended 0.750 m.

2. A soccer ball of diameter 22.6 cm and mass 426 g rolls up a hill without slipping, reaching a maximum height of 5.00 m above the base of the hill. We can model this ball as a thin-walled hollow sphere. A) At what rate was it rotating at the base of the hill? b) How much rotational kinetic energy did it then have?

3. A basketball rolls down a mountainside into a valley and then up the opposite side, starting from rest at a height H0 above the bottom. The rough part of the terrain prevents slipping while the smooth part has no friction. a) How high, in terms of H0, will it go up the other side? b) Why doesn’t the ball return to height H0? Has it lost any of its original potential energy?