1) When a compact disk with a 12.0-cm diameter is rotating at 4.74 rad/s , what

Question

1) When a compact disk with a 12.0-cm diameter is rotating at 4.74 rad/s , what are the linear speed and the centripetal acceleration of a point on its outer rim?

2) A Ferris wheel with a radius of 9.9 m rotates at a constant rate, completing one revolution every 34 s. Find the magnitude of a passenger's acceleration at the top of the wheel then at the bottom of the wheel.

3) A person swings a 0.53 kg tether ball tied to a 4.5 m rope in an approximately horizontal circle. A) If the maximum tension the rope can withstand before breaking is 11 N, what is the maximum angular speed of the ball? B) If the rope is shortened, does the maximum angular speed found in part A increase, decrease, or stay the same?

Explanation / Answer

1) linear speed =wr =4.74*0.06 = 0.2844 m/s

Centripetal acceleration = w^2r

= 4.74*4.74*0.06 =1.348 m/s2

2) w = 2pi/34 =0.1847 rad/s

Magnitude of acceleration will be same at the top and at the bottom since Ferry is moving with constant speed

a = w^2r = 0.1847^2 *9.9 = 0.338 m/s2

3) A) centripetal force is provided by tension T

T= mw^2r

W = sqrt(T/mr) = sqrt(11/(0.53*4.5)) =2.15 rad/s

B) If rope is shortened, r decreases, w increases. Hence maximum angular speed increases

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