# What is angular momentum?

justaguide | College Teacher | (Level 2) Distinguished Educator

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The angular momentum of a body is defined with reference to a chosen point also called the origin. Angular momentum of a body is a cross product given by L = r x p, where r is the position vector of the body about the point chosen as origin and p is the linear momentum of the body. As linear momentum is a cross product of two vectors, it is a vector too and acts in a direction that is given by the right hand rule.

Angular momentum is expressed in the units N*m*s.

The angular momentum of a rotating body has many applications; a gyroscope does not fall over due to its angular momentum, a moving bicycle is stable and does not tip over due to the angular momentum of its wheels.

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wanasyraf | Student, Grade 9 | (Level 3) eNoter

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angular momentum is moment of momentum, or rotational momentum is a conserved vector that states a particular measurable property of an isolated physical system does not change as the system evolves quantity that can be used to describe the overall state of a physical system. The angular momentum L of a particle with respect to some point of origin is

where r is the particle's position from the origin, p = mv is its linear momentum, and × denotes the cross product.

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 fins of a ceiling fan), the angular momentum can be expressed as the product of the body's moment of inertia I (a measure of an object's resistance to changes in its rotation rate) and its angular velocity ω:

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 moment of force,

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 star can also be explained in terms of angular momentum conservation.

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