Question

Sarah and Tom are riding on a merry-go-round revolving at a constant rate. Sarah is sitting on the edge and Tom is half-way in from the edge. What is the relationship between their centripetal acceleration?

Answer 1

Centripetal acceleration is given by the formula,

$a = \omega^2r$ ,
where a is the acceleration, $\omega$ is the angular velocity and r is the radial distance from the center of the rotation. Now for any instance $\omega$ is same for both of them, then, $a\propto r$ - acceleration and radial distance is directly proportional.

As Sarah's distance is twice of Tom's distance from center, then according to the proportionality rule, Sarah's centripetal acceleration is twice than tom.

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