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Systems of Particles and Rotational Motion — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsSystems of Particles and Rotational Motion5 Marks
Question
A disc rotating about its axis with angular speed $\omega_0$ 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 will the disc roll in the direction indicated?

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Answer

$\text{v}_{\text{A}}=\text{R}\omega_0,\text{ v}_\text{B}=\text{R}\omega_0,\text{ v}_\text{C}=\Big(\frac{\text{R}}{2}\Big)\omega_0$
The disc will not roll,
Angular speed of the disc $=\omega_0$
Radius of the disc = R
Using the relation for linear velocity, $\text{v}=\omega_0\text{R}$
For point A:
$\text{v}_{\text{A}}=\text{R}\omega_0,$ in the direction tangential to the right.
For point B:
$\text{v}_{\text{B}}=\text{R}\omega_0,$ in the direction tangential to the left.
For point C:
$\Big(\frac{\text{R}}{2}\Big)\omega_0$ 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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