Question

A purse at radius 2.00 m and a wallet at radius 3.00m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is (2m/s2)ˆi+(4.00 m/s2)ˆj.

(a) What is the acceleration of the wallet?

(b) For what coefficient of friction will the purse just start to slide?

(c) Assuming constant angular acceleration equal to that of the instant shown, how long has it been since the merry-go-round was at rest?

Answer 1

a] Magnitude of acceleration of the purse is:

acceleration of the purse is given by:

where r = 2 m

therefore, the angular velocity of the merry-go-round is:

so, the acceleration of the wallet will be:

b] The purse will start to slide when the centripetal force equals the force of friction.

=> .

c] Use

for the purse,

=> t = 0.67s.

This is the time since the merry-go-round was at rest.