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 8.00 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 6.00 rev/s. (a) which rate of rotation gives the greater speed for the ball?

6.0 rev/s gives greater speed for the ball.

Explanation:

given,

rotate a ball at the rate of = 8 rev/s

length of chain = 0.6 m

length increase to = 0.9 m

ball able to rotate  = 6 rev/s

(a) v = ω R                            

when R = 0.60                       ω = 8×2π            

v = 0.60 × 8 × 2π = 30.16 m/s                  

when R = 0.90                       ω = 6.00 × 2π    

v = 0.90 × 6.00 × 2π = 33.93 m/s                  

hence, 6.0 rev/s gives greater speed for the ball.

divide the right side by the left side

0.024÷1.2=0.02 for example