# Q7.28  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 ?

Let the angular speed of the disc is  $\omega$.

So the linear velocity can be written as    $v\ =\ \omega r$

(a)  Point A:-

The magnitude of linear velocity is $\omega r$ and it is tangentially rightward.

(b)  Point B:-

The magnitude linear velocity is $\omega r$ and its direction is tangentially leftward.

(c) Point C:-

The magnitude linear velocity is   $\frac{ \omega r}{2}$  and its direction is rightward.

The disc cannot roll as the table is frictionless.

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