## Friday, March 4, 2016

### Conservation of Angular Momentum and Applications

Angular momentum

Angular momentum is a physical quantity of rotational motion to understand about the rotation of the body. Angular momentum explains the impact of the torque on the body to rotate. Angular momentum is similar to the linear momentum of a body in translatory motion. Angular momentum explains the ability of a body to transfer rotational kinetic energy to other bodies during its interaction with the other bodies.

Angular momentum is defined as the moment of momentum. It means the product of momentum of the body and the perpendicular distance of the body from the axis of rotation. It could be said as the vector product of distance of the body from axis of rotation and momentum of the body. It means it is the product of two vectors and the result is also a vector quantity that has both magnitude and direction.

Angular momentum is equal to the magnitude of the product of the mass of the body, linear velocity and the distance of the particle from the axis of rotation. We can rewrite the magnitude of the linear velocity as the product of the distance of the body from axis of rotation and the angular velocity of the body. So we can rewrite the angular momentum as the product of the moment of inertia and angular velocity.

Conservation of Angular Momentum

Angular momentum of a system in rotational motion is always conserved when no external torque is acting on it. We can define torque as the rate of change of angular momentum. When torque is not acting, we can equate the rate of change of angular momentum can be equated to zero. It means change in angular momentum with respect to time is not there when there is no torque is acting on it. It means angular momentum of the system is zero. It means when no external torque is acting on the system, angular momentum of the system remains constant.

Law of conservation of any system is always conserved for all the bodies in rotational motion when no external torque is acting on it.

Applications of Law of conservation of Angular Momentum

Spin on Turn Table

We can explain law of conservation of angular momentum using some simple examples. Let us consider a ballet dancer rotating on a rotating disc. If he wants to increase his speed without any external torque, he can do it using conservation of angular momentum. Let he folds his hands and legs near to his spine and it is his axis of rotation on the rotating floor. There is no external support of torque acting on him in any manner. As he folds his body parts close to axis of rotation, hence his moment of inertia decreases.

We know as per law of conservation of angular momentum, it is conserved and it is the product of moment of inertia and angular velocity of the body. As the moment of inertia decreases, its angular velocity automatically increases to conserve angular momentum. So he starts rotating with more angular velocity. The vice versa is also possible and by moving the hands and legs away from axis of rotation, his moment of inertia increases and angular velocity increases.

Diving from spring board

Let us consider diving sport. Sports person jumps from spring board into air and finally lands into the water. He will be the winner if he makes more acrobatics in air like somersaults. There is no external torque supporting him anyway. He has to increase his angular speed himself to make more somersaults. He folds in hand and legs close to the stomach as it are his axis of rotation in the jump. Thus the distance of the body parts from axis of rotation decreases and hence moment of inertia also decreases. As angular momentum is conserved, his angular velocity increases and hence he can make more number of somersaults.

When he reaches near the bottom of the swimming pool, he shall reduce his speed. If not, he will land in with risky speed and it may cause injury to him. To avoid it, he opens his hands and legs away from the axis of rotation, his moment of inertia increases and hence angular momentum decreases.

Below is the detailed video lesson regarding conservation of angular momentum and its applications.

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