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 accelerations

Answer 1

The centripetal acceleration of Tom sitting half-way from the edge of the merry-go-round is double of the centripetal acceleration of Sarah sitting at the edge of the merry-go-round.

Let the constant rate of their motion, = v

Let the radius of the merry-go-round = R

The centripetal acceleration of Sarah sitting at the edge of the merry-go-round is calculated as;

$a_c_1 = \frac{V^2}{R}$

The centripetal acceleration of Tom sitting half-way from the edge of the merry-go-round is calculated as;

$a_c_2 = \frac{V^2}{\frac{1}{2} \times R } \\\\a_c_2 = \frac{2V^2}{R} \\\\a_c_2 = 2(\frac{V^2}{R} )\\\\a_c_2 = a_c_1$

Thus, the centripetal acceleration of Tom sitting half-way from the edge of the merry-go-round is double of the centripetal acceleration of Sarah sitting at the edge of the merry-go-round.

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