5. A Phonograph turntable rotates at a constant rate of 45 revolution per minute

Question

5. A Phonograph turntable rotates at a constant rate of 45 revolution per minute when rotating at full speed. A 20 gram mass is placed on this phonograph 10 cm away from the center of the phonograph as shown on the diagram below. a. What is the angular speed of the phonograph is radians per second? b. What is the linear speed of the 20 gram mass in cm/sec? c. What is the minimum coefficient of static friction required to keep the 20 gram mass moving in a circle? d. Now assume that the turntable motor is switched off, and that it takes 5 seconds to come to a complete stop. What is the angular acceleration (assumed constant) of the turntable as it comes to a stop (in radians/s^2)? e. How many revolutions does the turntable make before coming to a complete stop?

Explanation / Answer

part a )

45 rev/min = 45 * 2pi rad/60 s = 4.712 rad/s

part b )

v = rw

v = 10 * 4.712 = 47.12 cm/s

part c )

centripetal force = friction force

mv^2/r = mu*m*g

v = sqrt(mu*r*g)

0.4712 m/s = sqrt(mu*r*g)

0.4712^2 = mu*0.1 * 9.8

mu = 0.22656

part d )

wf = wi + alpha*t

alpha= -wi/t

alpha = -4.712 / 5 = -0.9424 rad/s^2

part e )

wf^2 = wi^2 + 2*alpha*theta

wf = 0

0 = 4.712^2 - 2 * 0.9425 * theta

theta = 11.78 rad = 1.8748 rev

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