An athlete swings a ball, connected to the end of a chain, in a horizontal circle. the athlete is able to rotate the ball at the rate of 8.13 rev/s when the length of the chain is 0.600 m. when he increases the length to 0.900 m, he is able to rotate the ball only 6.04 rev/s. (a) which rate of rotation gives the greater speed for the ball? 6.04 rev/s 8.13 rev/s (b) what is the centripetal acceleration of the ball at 8.13 rev/s? m/s2 (c) what is the centripetal acceleration at 6.04 rev/s? m/s2

(a) 6.04 rev/s

The speed of the ball is given by:

where

is the angular speed

r is the distance of the ball from the centre of the circle

In situation 1), we have

r = 0.600 m

So the speed of the ball is

In situation 2), we have

r = 0.900 m

So the speed of the ball is

So, the ball has greater speed when rotating at 6.04 rev/s.

(b)

The centripetal acceleration of the ball is given by

where

v is the speed

r is the distance of the ball from the centre of the trajectory

For situation 1),

v = 30.6 m/s

r = 0.600 m

So the centripetal acceleration is

(c)

For situation 2 we have

v = 34.1 m/s

r = 0.900 m

So the centripetal acceleration is