Question

A disc rotating about its axis with angular speed ω_ois 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

v_A = Rω_o; v_B = Rω_o; ; The disc will not roll

Angular speed of the disc = ω_o

Radius of the disc = R

Using the relation for linear velocity, v = ω_oR

For point A:

v_A = Rω_o; in the direction tangential to the right

For point B:

v_B = Rω_o; in the direction tangential to the left

For point C:

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.