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Question

A cylinder rotating at an angular speed of 50 rev/s is brought in contact with an identical stationary cylinder. Because of the kinetic friction, torques act on the two cylinders, accelerating the stationary one and decelerating the moving one. If the common magnitude of the angular acceleration and deceleration be 1rev/s2, then how much time (in s) will it take before the two cylinder have equal angular speed.

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Solution

Given: Initial velocity =50rev/s,α=1rev/s2
Let final velocity =ω2rev/sec
Let time taken =t
For first cylinder
ω2ωαtω2=50t
For second cylinder
ω2=0αt50t=αt50=2tt=25sec

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