Engineering
Physics
Rolling
Newtons Second Law of Motion
Static and Kinetic Friction
Question

A disc of radius R is spun to an angular speed w0 about its axis and then imparted a horizontal velocity of magnitude ω0R4 (at t = 0) with its plane remaining vertical. The coefficient of friction between the disc and the plane is sufficient to allow pure rolling, once it starts. The sense of rotation and direction of its linear speed are shown in the figure. Choose the correct statement.

Generated image

The disc will stop finally irrespective of value of v and ω.

The disc will return to its initial position.

if v0 = ω0 R/2 then the disc will stop.

The friction will act in rightward direction after the rolling (without slipping) starts.

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Solution
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(A) Li = mv0R = Icω0

=mω0R4R−12mR2ω0=−mω0R24

Since Li is –ve

∴it will return to its initial position.