ï»¿ A disc rotating about its axis with angular speed Ï‰ois placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc isÂ 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? from Physics System of Particles and Rotational Motion Class 11 Manipur Board

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A disc rotating about its axis with angular speed Ï‰ois placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc isÂ 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?

Angular speed of the disc = Ï‰oÂ

Radius of the disc =Â RÂ

Using the relation for linear velocity,Â vÂ = Ï‰oRÂ

For point A:Â

vAÂ =Â RÏ‰o,Â in the direction tangential to the right.

For point B:Â

vBÂ =Â RÏ‰o,Â in the direction tangential to the left.Â

For point C:

vcÂ = Ï‰o,Â in the direction same as that ofÂ vA.

vAÂ =Â RÏ‰o;Â

vBÂ =Â RÏ‰0,Â

vcÂ =Â Ï‰0
The disc will not roll.

The directions of motion of points A, B, and C on the disc are shown in the following figureÂ

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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Define centre of mass.

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The position of the centre of mass is calculated using the usual Newtonian type of equations of motion.Â
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What is the need of centre of mass?

Newtonâ€™s second law of motion is strictly applicable to point masses only. To apply the Newton's law of motion to rigid bodies, the concept of centre of mass is introduced.

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