Angular momentum is a fundamental concept in physics that describes the rotational motion of an object. It is defined as the product of the moment of inertia and the angular velocity of the object. In the case of a particle rotating with a central force, the angular momentum is constant due to zero torque.

Explanation:
Zero Torque:
- Torque is a measure of the tendency of a force to rotate an object around a specific axis. It is defined as the cross product of the force and the distance from the axis of rotation.
- In the case of a particle rotating with a central force, the force is directed towards or away from the center of rotation, and the distance from the axis of rotation is always perpendicular to the force.
- Since the cross product of two perpendicular vectors is zero, the torque exerted by the central force on the particle is zero.
- Therefore, the angular momentum of the particle remains constant, as there is no external torque acting on it to change its rotational motion.

Constant Angular Momentum:
- Angular momentum is a conserved quantity in the absence of external torques.
- When there is no external torque acting on a rotating object, its angular momentum remains constant.
- This is known as the law of conservation of angular momentum.
- In the case of a particle rotating with a central force, the absence of torque implies that the angular momentum of the particle is constant.
- This means that the moment of inertia and the angular velocity of the particle remain constant throughout its rotation.
- The conservation of angular momentum has various applications in physics, such as explaining the behavior of rotating systems, orbits of celestial bodies, and the stability of rotating objects.

Conclusion:
The angular momentum of a particle rotating with a central force is constant due to zero torque. This is because the force acts along the radial direction, and the distance from the axis of rotation is always perpendicular to the force, resulting in zero torque. The conservation of angular momentum is a fundamental principle in physics and has wide-ranging applications in various fields.