Angular momentum

In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important quantity in physics because it is a conserved quantity – the angular momentum of a system remains constant unless acted on by an external torque.

The definition of angular momentum for a point particle is a pseudovector r×p, the cross product of the particle's position vector r (relative to some origin) and its momentum vector p = mv. This definition can be applied to each point in continua like solids or fluids, or physical fields. Unlike momentum, angular momentum does depend on where the origin is chosen, since the particle's position is measured from it. The angular momentum of an object can also be connected to the angular velocity ω of the object (how fast it rotates about an axis) via the moment of inertia I (which depends on the shape and distribution of mass about the axis of rotation). However, while ω always points in the direction of the rotation axis, the angular momentum L may point in a different direction depending on how the mass is distributed.

Angular momentum is additive; the total angular momentum of a system is the (pseudo)vector sum of the angular momenta. For continua or fields one uses integration. The total angular momentum of anything can always be split into the sum of two main components: "orbital" angular momentum about an axis outside the object, plus "spin" angular momentum through the centre of mass of the object.

Torque can be defined as the rate of change of angular momentum, analogous to force. The conservation of angular momentum helps explain many observed phenomena, for example the increase in rotational speed of a spinning figure skater as the skater's arms are contracted, the high rotational rates of neutron stars, the falling cat problem, and precession of tops and gyros. Applications include the gyrocompass, control moment gyroscope, inertial guidance systems, reaction wheels, flying discs or Frisbees and Earth's rotation to name a few. In general, conservation does limit the possible motion of a system, but does not uniquely determine what the exact motion is.

...
Wikipedia