Question

A disc rotating about its axis with angular speed ${\omega }_0$ 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?

Answer 1

Radius of the disc = R
Using the relation for linear velocity, $v={\omega }_{0}R$
For point A:
$v_A=R{\omega }_0$; in the direction tangential to the right
For point B:
$v_B=R{\omega }_0$; in the direction tangential to the left
For point C:
$v_c=\left(\frac{R}{2}\right){\omega }_0;$ in the direction same as that of $v_A$
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.