<P> 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 . </P> <P> 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 . </P> <P> 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 . </P> <P> In quantum mechanics, angular momentum is an operator with quantized eigenvalues . Angular momentum is subject to the Heisenberg uncertainty principle, meaning that only one component can be measured with definite precision; the other two cannot . Also, the "spin" of elementary particles does not correspond to literal spinning motion . </P>

Applications of the principle of conservation of angular momentum
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