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Angular momentum is a quantity that is useful in describing the rotational state of a physical system. For a rigid body rotating around an axis of symmetry (e.g. the fins of a ceiling fan), the angular momentum can be expressed as the product of the body's moment of inertia (a measure of an object's resistance to changes in its rotation rate) and its angular velocity. In this way, angular momentum is sometimes described as the rotational analog of linear momentum.Angular momentum is conserved in a system where there is no net external torque, and its conservation helps explain many diverse phenomena. For example, the increase in rotational speed of a spinning figure skater as the skater's arms are contracted is a consequence of conservation of angular momentum. The very high rotational rates of neutron stars can also be explained in terms of angular momentum conservation. Moreover, angular momentum conservation has numerous applications in physics and engineering (e.g. the gyrocompass).Formally, the angular momentum of a point object is defined as the cross product of the object's position vector and linear momentum vector The angular momentum of a system of particles (e.g. a rigid body) is the sum of angular momenta of the individual particles.