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A disc rotating about its axis with angular speed wo is placed lightly (without any translational push) on a perfectly friction less 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.? Will the disc roll in the direction indicated?
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Quicker Maths

It will not roll as friction is needed for rolling.
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Quicker Maths

It will not roll as friction is needed for rolling. Velocity at A = Rw At B = Rw At C = (R/2)w
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vA = Rωo; vB = Rω0, vc = (R/2)ω0 The disc will not rollAngular speed of the disc = ωo Radius of the disc = RUsing the relation for linear velocity, v = ωoRFor point A:vA = Rωo; in the direction tangential to the rightFor point B:vB = Rωo; in the direction tangential...
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vA = RωovB = Rω0, vc = (R/2)ω0

The disc will not roll
Angular speed of the disc = ω
Radius of the disc = R
Using the relation for linear velocity, v = ωoR
For point A:
vA = Rωo; in the direction tangential to the right
For point B:
vB = Rωo; in the direction tangential to the left
For point C:
vc = (R/2)ωo in the direction same as that of vA

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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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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