(from Ohanian) The outer edge of the grooved area of a long-playing record is at

Question

(from Ohanian) The outer edge of the grooved area of a long-playing record is at a radial distance 34 cm from the center; the inner edge is at a radial distance of 20 cm. The record rotates at 4.2 rev/min. The needle of the pick-up arm takes 2.7 minutes to move uniformly from the outer edge to the inner edge.

What is the radial speed of the needle?  m/s
What is the speed of the outer edge relative to the needle?  m/s
What is the speed of the inner edge relative to the needle?  m/s
Suppose the phonograph is turned off, and the record uniformly and stops rotating after 10 s. What is the angular acceleration?  rad/s2

Explanation / Answer

a)
radial speed = speed along the radius = d / t = (0.34 - 0.20)m / 2.7*60s
radial speed = 0.00086 m/s

b)
w = 4.2*2pi rad / 60s = 0.44 rad/s
Outer edge speed is v = r*w
v = 0.34m * 0.44 rad/s
v = 0.15 m/s

c)
Inner edge speed is v = r*w
v = 0.14m * 0.44 rad/s
v = 0.062 m/s

d)
accel = dw / dt = 0.44 rad/s / 10s
a = 0.044 rad/s^2

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