﻿ A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring. the ring will then rotate with an angular velocity from Physics System of Particles and Rotational Motion Class 11 Manipur Board

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System of Particles and Rotational Motion

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A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring. the ring will then rotate with an angular velocity

• • • • B. Applying law of conservation of angular momentum.
I1ω1 = I2ω2

In the given case
I1 = MR2
I2 = MR2 + 2mR2

ω1

then ω2 = I1ω /I2 = Mω / M +2m

Applying law of conservation of angular momentum.
I1ω1 = I2ω2

In the given case
I1 = MR2
I2 = MR2 + 2mR2

ω1

then ω2 = I1ω /I2 = Mω / M +2m

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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.
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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.
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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.
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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.
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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.
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