Physics 207 WebPages - Fall 1999

Problem 4 (Problem 43 in Textbook)

A phonograph turntable is rotating at 33¹/₃ rev/min. A small object is on the turntable 6.0 cm from the axis of rotation.

Calculate the acceleration of the object, assuming that the object does not slip

Solution:

The magnitude of the linear velocity is not changing; however, the direction is. In this case, the radial component of linear acceleration is responsible of the change in the direction of the linear velocity.

(b) What is the minimum value of the coefficient of static friction between the object and the turntable?

Solution:

If the object does not slip, the static frictional force, which opposes the rotational motion by pulling away from the center in this case, has to be at least equal to the centripetal force, which pulls toward the center.

(c) Suppose that the turntable achieved its angular speed by starting from rest and undergoing a constant angular acceleration for 0.25 s. Calculate the minimum coefficient of static friction required for the object not to slip during the acceleration period.

Solution:

We first find the constant angular acceleration.

We then convert the angular acceleration to the tangential acceleration. The static frictional force, which acts opposite of the applied force, has to be at least equal to the tangential force at that moment of rotation.

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