Circular Motion Review Problems

1. A children's carousel rotates 3 times every 2 seconds. The diameter of the carousel is 3.0 meters.

a. What is the period of motion?
b. What is the tangential velocity of the carousel?
c. What is the centripetal acceleration of the rider at the edge of the carousel?

2. When traveling down the road at a constant speed of 55 mph, 26.4 m/s, the tangential velocity of the wheels is also 55 mph.  If a car tire is 65.0 cm in diameter, then;

a. What is the period and frequency of the spinning car tire?
b. What is the centripetal acceleration of a rock stuck in the tire’s tread?

3.   Given that the Earth is 1.49x10¹¹ m from the Sun. And the earth's period of motion is 365.25 days. Calculate how fast it is revolving around the Sun. Put your answer in m/s.

4.   Do the same thing for the Moon: Given it is 3.8x10⁸ m from the Earth and revolves around the Earth every 27.31 days. Put your answer in m/s.

5.  Given the Earth has a mass of 5.98x10²⁴ kg and the Moon has a mass of 7.34x10²² kg, what centripetal force is necessary to keep each in orbit.

6.   A bicycle wheel of radius 0.325 m rotates at a speed of 10.0 m/s (22.4 mph).
a. If a person is riding the bike, how fast are they traveling
b. What is the frequency and period of rotation of the bicycle's wheel?

7.   The time shaft ride at King's Dominion has a radius of 5.0 m and spins with a period of 1.3 seconds (only a guess).
a.What is the tangential velocity of the ride?
b. What is the centripetal acceleration of the ride?
c. What must the ride’s period of motion be for the ride to spin to give the rider a centripetal acceleration of 2.0 g’s?

34.   While playing "Bolo Master of the World" little Lisa was spinning a rock around her head on a string 1.32 m long. The rock travels around once every 1.43 seconds.
         a. What is the speed of the rock?
         b. What is the centripetal acceleration of the rock?
         c. If the rock has a mass of 0.15 kg then, what is the centripetal force acting on the rock?