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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 solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s–1. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

Mass of the cylinder, m = 20 kg 

Angular speed, ω = 100 rad s–1 

Radius of the cylinder, r = 0.25 m 

The moment of inertia of the solid cylinder, 

   I = mr2 / 2 

     = (1/2) × 20 × (0.25)

     = 0.625 kg m

∴ Kinetic energy = (1/2) I ω

                      = (1/2) × 6.25 × (100)2 

                      = 3125 J 


Angular momentum, L = Iω 

                               = 6.25 × 100 

                               = 62.5 Js 

That is, there is a magnitude of 62.5 Js angular momentum of the cylinder about it's axis. 

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 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.

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. 

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. 

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.