Question

A girl and a boy are riding on a merry go round that is turning at a constant rate. The girl is near the outer edge, and the boy is closer to the center. Who has greater tangential acceleration?Both the girl and boy have the same nonzero tangential accelerationThe boy has greater tangential accelerationBoth the girl and the boy have zero tangential accelerationThe girl has greater tangential acceleration

Answer 1

The girl has greater tangential acceleration

Step-by-step explanation:

The angular acceleration (
`\alpha`) of the merry go round is equal to the rate of the change of the angular velocity,
`\omega`:

`\alpha = (d\omega)/(dt)`

Since all the points of the merry go round complete 1 circle in the same time, the angular velocity of each point of the merry go round is the same, and so all the points also have the same angular acceleration.

The tangential acceleration instead is given by

`a_t = \alpha r`

where

`\alpha` is the angular acceleration

r is the distance from the centre of the merry go round

Since the girl is near the outer edge and the boy is closer to the centre, the value of r for the girl is larger than for the boy, so the girl has greater tangential acceleration.