Answer
(a) The child who is 4 m away from the axis of rotation has a larger linear speed.
(b) The child who is 4 m away from the axis of rotation has a larger acceleration.
(c) The angular speed for each child is equal.
(d) The angular displacement for each child is equal.
Work Step by Step
(a) The child who is 4 m away from the axis of rotation has a larger linear speed because this child moves a larger distance per unit of time.
(b) Let $T$ be the time of one revolution. We can find an expression for the centripetal acceleration.
$v = \frac{2\pi~r}{T}$
$a_c = \frac{v^2}{r} = \frac{(\frac{2\pi~r}{T})^2}{r} = \frac{4\pi^2~r}{T^2}$
The child who is 4 m away from the axis of rotation has a larger acceleration.
(c) Since each child rotates through the same angle per unit time, the angular speed for each child is equal.
(d) Since each child rotates through the same angle per unit time, the angular displacement for each child is equal.
