Question

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 7.56 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 6.22 rev/s.
Required:
a. Which rate of rotation gives the greater speed for the ball?
b. What is the centripetal acceleration of the ball at 8.16 rev/s?
c. What is the centripetal acceleration at 6.35 rev/s?

Answer 1

Answer:

a) $\omega _1=7.56rev/s=>47.5rads/s$

b) $a=30.7$

c) $a=35.91$

Explanation:

From the question we are told that:

Initial angular velocity $\omega _1=7.56rev/s=>47.5rads/s$

Initial Length $L_1=0.600m$

Final angular velocity $\omega _2=6.22rev/s=39rad/s$

Final Length $L_2=0.900m$

a)

Generally the rotation with the greater speed is

$\omega _1=7.56rev/s=>47.5rads/s$

b)

Generally the equation for centripetal acceleration at 8.16 is mathematically given by

$a=\omega_1^2*L_1$

$a=8.16 rev/s*0.6$

$a=30.7$

c)

At 6.35 rev/s

$a=6.35 rev/s*0.9$

$a=35.91$