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System of Particles and Rotational Motion

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12

A circular platform is mounted on the frictionless vertical axle. Its radius R =2 m and its moment of inertia about the axle is 200 kg m2. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 ms-1 relative to the ground. Time taken by the man to complete one revolution is

  • π sec

  • 3π/2 sec

  • 2π sec

  • π/2 sec


A.

π sec

For conservation of angular momentum

Iω space equals space mvr
200 space straight x space straight omega space equals space 50 space straight x space 2 space straight x space 1
space straight omega space equals space 1 half space rad divided by straight s
straight v equals space rω space equals space 1 space straight m divided by straight s
straight T equals space fraction numerator 2 πr over denominator 1 minus left parenthesis negative 1 right parenthesis end fraction space equals space fraction numerator 2 πr over denominator 2 end fraction space equals space πr space sec

For conservation of angular momentum

Iω space equals space mvr
200 space straight x space straight omega space equals space 50 space straight x space 2 space straight x space 1
space straight omega space equals space 1 half space rad divided by straight s
straight v equals space rω space equals space 1 space straight m divided by straight s
straight T equals space fraction numerator 2 πr over denominator 1 minus left parenthesis negative 1 right parenthesis end fraction space equals space fraction numerator 2 πr over denominator 2 end fraction space equals space πr space sec

2312 Views

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. 
943 Views

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.
730 Views

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. 
1449 Views

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. 
911 Views

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. 
794 Views