Ncert Exercises & Solutions

Question 7. 28. A disc rotating about its axis with angular speed $ω_{0}$ 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.? Will the disc roll in the direction indicated?

v_{A} = {Rω}_{0}; v_{B} = {Rω}_{0}; v_{c} = (\frac{R}{2}) ω

; 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:

v_{c} = (\frac{R}{2}) ω_{o}

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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