Question 7. 28. A disc rotating about its axis with angular speed ω0 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.? Will the disc roll in the direction indicated?


vA=0;vB=0; vc = R2ω
; The disc will not roll
The angular speed of the disc = ωo
The radius of the disc = R
Using the relation for linear velocity, v = ωoR
For point A:
vA = Rωo; in the direction tangential to the right
For point B:
vB = Rωo; in the direction tangential to the left
For point C:
vc=(R2)ωo in the direction same as that of vA
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.