Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

Angular momentum

In physics, angular momentum, moment of momentum, or rotational momentum is a vector quantity that represents the product of a body's rotational inertia and rotational velocity about a particular axis. The angular momentum of a system of particles (e.g. a rigid body) is the sum of angular momenta of the individual particles. For a rigid body rotating around an axis of symmetry (e.g. the blades of a ceiling fan), the angular momentum can be expressed as the product of the body's moment of inertia, I, (i.e. a measure of an object's resistance to changes in its rotation rate) and its angular velocity ω:

mathbf{L} = I oldsymbol{omega} , .

In this way, angular momentum is sometimes described as the rotational analog of linear momentum.

For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as the magnitude of its linear momentum, mv, multiplied by the radial distance, r. Thus, the angular momentum L of a particle with respect to some point of origin is

mathbf{L} = mmathbf{v}r

where r is the particle's distance from the origin and mv is its 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).

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