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Question

A body is moving down into a well through a rope passing over a fixed pulley of radius 10 cm. Assume that there is no slipping between rope & pulley, calculate the angular velocity and angular acceleration of the pulley at an instant when the body is going down at a speed of 20 cm/s and has an acceleration of 4.0 m/s2

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Solution

Radius, r=10 cm=10×102 m
Linear velocity, V=20 cm/s=20×102 m/s
Angular acceleration, ω=Vr
ω=20×10210×102
ω=2 rad/s
Angular acceleration, a=V2r
a=400×10410×102
a=40×102 rad/s2

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