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System of Particles and Rotational Motion

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Physics Part I

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12
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?

Angular speed of the disc = ω

Radius of the disc = 

Using the relation for linear velocity, v = ωo

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 = open parentheses straight R over 2 close parenthesesωo, in the direction same as that of vA.

vA = Rωo

vB = Rω0

vc = open parentheses straight R over 2 close parenthesesω0
The disc will not roll.

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.

Is it necessary that there should be matter at the centre of mass of system?

No, it is not necessary that there be matter at the centre of mass of the system.

For e.g., if two equal point masses are separated by certain distance, the centre of mass lies at the mid point of two point masses and there is no mass at that point.

What is the significance of defining the center of mass of a system?

The motion of n particle system can be reduced to one particle motion.

An equivalent single point object would enable us to discuss the overall motion of the system. 

Define centre of mass.

Centre of mass of a body or a system of bodies is a point at which the entire mass of the body or system is supposed to be concentrated. 

What is the need of centre of mass?

Newton’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.

The concept of centre of mass of a system enables us to discuss overall motion of the system by replacing the system by an equivalent single point object. 

Is it necessary for centre of mass to lie within the body?

No, centre of mass needs not to lie within the body. It is not necessary that the total mass of the system be actually present at the centre.

The position of the centre of mass is calculated using the usual Newtonian type of equations of motion.