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Bob and his sister Alice are having a ride on a merry-go-round which spins with a...

Bob and his sister Alice are having a ride on a merry-go-round which spins with a constant angular speed. Alice is two times closer to the axis of rotation. Compare the magnitudes of her acceleration aA (in m/s^2) to Bob's acceleration aB
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Answer #1

Let be the angular speed of merry-go-round. The centripetal acceleration of a point at distance r from the axis of rotation is

Given Alice is two times closer to axis of rotation than Bob or in other words, Bob is two times farther away from the axis of rotation than Alice

The ratio of accelerations is

Using rB=2rA

The acceleration of Alice is half the acceleration of Bob.

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