1. A merry go round 2.4 meters in diameter spins at 20 rpms. What is the instant

Question

1. A merry go round 2.4 meters in diameter spins at 20 rpms. What is the instantaneous speed of a rider sitting on the edge?


A. What is the instantaneous speed of a rider sitting 0.30 meters from the axis of rotation on the example in #1?

B. A baseball is whirled at the end of a string 2.3 meters long. If the ball has a speed of 25m/s, how many rpms is the baseball doing?


C. How many rpms in #3 if the ball moves at 35m/s?

D. How many rpms if the ball moves at 20 m/s and the string is shortened to 1.5 m?

Explanation / Answer

(A) (1) Diameter d = 0.30 m Radius r = 0.15 m n = 20 rpms = (20/60) rps Angular speed ? = 2pn = 2p(20/60) = 2.094 Instantaneous speed v = r? = 0.15 * 2.094 = 0.314 m/s (2)Given r = 0.3 m Instantaneous speed v = r? = 0.3 * 2.094 = 0.6282 m/s (B) r = 2.3 m v = 25 m/s number of revolutions n = 60v/2pr = (25)/(2*3.141*2.3)                                                      = 103.8 rpms (C) r = 2.3 m v = 35 m/s number of revolutions n = 60v/2pr = (60*35)/(2*3.141*2.3)                                                      = 145.32rpms (D) r = 1.5 m v = 20 m/s number of revolutions n = 60v/2pr = (60*20)/(2*3.141*1.5)                                                      = 127.34 rpms    number of revolutions n = 60v/2pr = (60*20)/(2*3.141*1.5)                                                      = 127.34 rpms

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