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Question

A disc rotating about its axis with angular speed ω0 is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is R. What are the linear velocities of the points A, B and C on the disc shown in Fig. 7.41? Will the disc roll in the direction indicated?

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Solution

Radius of the disc = R
Using the relation for linear velocity, v=ω0R
For point A:
vA=Rω0; in the direction tangential to the right
For point B:
vB=Rω0; in the direction tangential to the left
For point C:
vc=(R2)ω0; in the direction same as that of vA
The directions of motion of points A, B, and C on the disc are shown in the following figure

Since the disc is placed on a frictionless table, it will not roll. This is because the presence of friction is essential for the rolling of a body.


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