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Conservation Of angular momentum is considered one the most difficult concept.
12 Questions around this concept.
A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity . Two objects each of mass M are attached gently to the opposite ends of the diameter of the ring. The ring now rotates with an angular velocity
=
Analogy Between Translatory Motion and Rotational Motion for common terms
|
Translatory motion |
Rotatory motion |
1 |
Mass (m) |
Moment of Inertia (I) |
2 |
Linear momentum |
Angular Momentum |
3 |
Force F=ma |
Torque |
From we get
i.e. the rate of change of angular momentum is equal to the net torque acting on the particle.
This is Rotational analogue of Newton's second law
Angular impulse =
Or,
i.e., Angular impulse is equal to change in angular momentum
As
So if the net external torque on a particle is zero then for that particle
Similarly in case of system consists of n particles
If the net external torque on a system is zero then for that system
Or,
I.e Angular momentum of a system remains constant if resultant torque acting on it zero.
This is known as the law of conservation of angular momentum.
For a system if then its
Or,
Example-In a circus during performance an acrobat try to bring the arms and legs closer to body to increase spin speed. On bringing the arms and legs closer to body, his moment of inertia I decreases. Hence increases.
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