Question

A disc rotating about its axis with angular speed ω₀ is placed lightly (without any transitional 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 the figure. Will the disc roll out in the direction indicated?

Answer 1

we know, Velocity of a point on a rolling disc is given by, v = $d\omega$
Where, d is distance from center of rotation.
ω is the angular velocity of the body.

Now, Velocity at points A and B are same. because distance between points A& B and centre of rotation = R.

as you can see velocity at A , $v_A=R\omega_0$

velocity at B, $v_B=R\omega_0$


now, velocity at C , $v_C$ = distance of C from centre of rotation . angular velocity

here, distance of C from centre of rotation = R/2

so, velocity at C , $v_C=\frac{R}{2}\omega_0$