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 8.44 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 5.95 rev/s.

(a) which rate of rotation gives the greater speed for the ball?
(b) what is the centripetal acceleration of the ball at 8.44 rev/s?
(c) what is the centripetal acceleration at 5.95 rev/s?

a) the greater speed for the ball is getting with the large radius of the circle. b) 1.68* 10 ^3 m/s^2 c) 1.25*10^3 m/s^2

Explanation: In order to solve this problem firstly we have to consider that speed in a of the circular movement is directly the angular rotation multiply the radius of the circle so by this we found that the second radius get large speed.

Secondly to calculate the centripetal acceleration for the ball we have to considerer the relationship given by:

acceleration in a circular movement= ω^2*r

so

a1= (8.44 *2*π)^2*r1=1.68 *10^3 m/s^2

a2= (5.95*2*π)^2*r2=1.25*10^3  m/s^2

most of them using statistics and defining how things are being measured