An earth satellite is moving in a circular motion due to change in the direction of velocity. Its angular momentum about centre is conserved as their is no external force acting on the system

Conservation of Angular Momentum in Circular Orbit

Angular momentum is a fundamental concept in physics that describes the rotational motion of an object. In the case of an earth satellite moving in a circular orbit, the angular momentum is conserved. Let's understand why.

Angular Momentum:
Angular momentum is defined as the product of the moment of inertia and the angular velocity of an object. It is a vector quantity and is given by the equation:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Conservation of Angular Momentum:
Conservation of angular momentum occurs when there is no net external torque acting on a system. This means that the total angular momentum of the system remains constant.

Circular Orbit:
When a satellite is moving in a circular orbit around the Earth, it experiences a gravitational force towards the center of the Earth. This force provides the necessary centripetal force for the satellite to maintain its circular path.

Explanation:
In a circular orbit, the angular velocity of the satellite remains constant. This is because the gravitational force acting on the satellite provides the required centripetal force, which keeps the satellite in a circular path. Since the angular velocity remains constant, the angular momentum of the satellite is also constant.

The gravitational force acting on the satellite is always directed towards the center of the Earth. This force does not produce any torque on the satellite because the torque is defined as the product of the force and the perpendicular distance from the axis of rotation. In a circular orbit, the force and the displacement (distance) are parallel, so the torque is zero.

Since the net external torque acting on the satellite is zero, the angular momentum of the satellite is conserved. This means that the angular momentum of the satellite remains constant throughout its motion.

Conclusion:
In a circular orbit, the angular momentum of an earth satellite is conserved. This is because there is no net external torque acting on the satellite. The gravitational force provides the necessary centripetal force to keep the satellite in its circular path, without producing any torque. Therefore, the angular momentum remains constant.