System of particles and Rotational motion NCERT Solutions Class 11 Physics - Solved Exercise Question 7.28

Question 7.28:
A disc rotating about its axis with angular speed ωois 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?

Solution:
vA = Rωo; vB = Rω0, vc = (R/2)ω0
The disc will not roll
Angular speed of the disc = ωo
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 = (R/2)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.

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