Question

Consider two children sitting on a merry-go-round, with one closer to the outer edge and one closer to the center. show answer No Attempt Which child has a greater angular speed?

Answer 1

Answer:

They both have the same angular speed.

Explanation:

The mathematical formula for angular speed is:

$w=\frac{2\pi}{T}$

where $w$ is angular speed, $2\pi$ is a constant, and $T$ is the period (the time it takes the marry-go-round to complete a lap).

What we can see from the formula is that, since the $2\pi$ does not change its value, the angular speed depends only on the period T.

In this case for both the children closer to the outher edge and for the children closer to the center, the time to complete a lap is the same, because the time does not depend on where they are sitting in the marry go round. This means that the period for both is the same.

Thus, since the period for both is the same, the angular speed given by

$w=\frac{2\pi}{T}$ will also be the same