An old-fashioned vinyl record rotates on a turntable at 33 1/3 rev/min. What is the linear speed at radius r?

An old-fashioned vinyl record rotates on a turntable at 33 1/3 rev/min while the phonograph needle travels on a track that spirals from the outside to the inside of the record. (a) What is the angular speed in rad/s? What is the linear speed of a point on the record at the needle at (b) the beginning and (c) the end of the recording? The distances of the needle from the turntable axis are 5.9 in and 2.9 in at these two positions.

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a) the angular speed is 33 1/3 rev/min which is (100/3)*2pi rad/min, equivalent to (100/3)*2pi/60 rad/second = 20/18*pi rad/s = 3.491 rad/s

b) use the formula relating angluar speed to linear speed

v = wr

where v is the linear speed, w the angular speed and r is the radius

If the radius is 5.9 inches, the linear speed is 3.491 * 5.9 = 20.59 inches/s

c) If the radius is 2.9 inches, the linear speed is 3.491 * 2.9 = 10.12 inches/s

**a) 3.49 rad/s b) 20.59 inches/s c) 10.12 inches/s**

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