Three children are playing on a roundabout (rotatable horizontal platform) at a playground. Child X is standing on the edge of the roundabout. This child is pushing so that the edge of the roundabout moves in a circle at a constant speed of

2.4 m s^{- 1}

, as shown in the view from above in Figure 1.1.

Figure 1.1, a view from above of a circular roundabout rotating anticlockwise, with child X at the rim moving at $2.4\text{ m s}^{-1}$, child Y at a distance $2R$ from the centre, child Z at a distance $R$ from the centre, and the roundabout's radius marked $3R$

The radius of the roundabout is

3 R

. Child Y is sitting on the roundabout at a distance

2 R

from the centre. Child Z is sitting at a distance

R

from the centre. Child Y is moving in a circle with an angular speed of

0.75 rad s^{- 1}

. Calculate the radius of the roundabout.

1(b)(ii)Circular MotionEasy2 marks

Calculate the frequency of rotation of the roundabout.

1(b)(iii)Circular MotionEasy2 marks

Calculate the centripetal acceleration of child Y.

1(c)Circular MotionMedium3 marks

For the roundabout in 1(b), compare the linear and angular velocities for child X and child Z at any instant in time.

For each of magnitude and direction of the two quantities, select the one comparison that applies.

Linear velocity: magnitude

Linear velocity: direction

Angular velocity: magnitude

Angular velocity: direction