14.9 : 力のモーメントと角運動量の関係

In a spinning top, applying a force at a distance from the center creates torque, which changes the angular momentum of the top, causing it to spin.

The moment of a force is the rotational equivalent of linear force. It measures how a force on an object induces rotation.

Angular momentum is the rotational analog of linear momentum and signifies the tendency of an object to continue rotating.

The time derivative of angular momentum gives an expression, in which the first term equals zero. The second term can be expressed in terms of the net force acting on the particle.

Comparing the expression with the moment of force equation establishes a relation between the angular momentum and the moment of force.

This relationship mirrors Newton's second law but for rotational motion.

This equation applies equally to the systems of particles or rigid bodies.

In a system of particles, each particle contributes to the overall angular momentum of the system.