Question

A disc rotating about its axis with angular speed wo 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

The velocity directions at points A, B and C are shown below.

The linear velocity of point A is,

v A =( OA ) ω 0

Here, OA is the radius of the disc.

Substituting R for OA in the above equation, we get:

v A =( R ) ω 0 =R ω 0

The direction of velocity at point A is tangential to the right direction.

The linear velocity of point B is,

v B =( OB ) ω 0

Here, OB is the radius of the disc.

Substituting R for OB in the above equation, we get:

v B =( R ) ω 0 =R ω 0

The direction of velocity at point B is tangential to the left direction.

The linear velocity of point C is,

v C =( OC ) ω 0

Here, OA is the distance of point C from point O.

Substituting R 2 for OC in the above equation, we get:

v C =( R 2 ) ω 0 = ω 0 R/2

The direction of velocity at point C is tangential to the right direction.

Since the disc is placed on frictionless table, it will not roll in the direction indicated. The velocity at the point of contact will not be zero in the absence of frictional force at the contact surface.