Angular Momentum

The angular momentum of a rigid object is defined as the product of the moment of inertia and the angular velocity. Angular momentum is the measure of the "quantity of motion. Angular momentum is associated with a particle in motion. The motion need not be rotational motion, but any motion. Importantly, it is measured with respect to a fixed point. It is analogous to linear momentum and is subject to the fundamental constraints of the conservation of angular momentum principle if there is no external torque on the object. Angular momentum is a vector quantity. If a system consists of several particles, the total angular momentum about an origin can be obtained by adding all the angular momenta of the constituent particles. Angular momentum can be calculated by multiplying the square of the displacement r, the mass of the particle and the angular velocity.It is derivable from the expression for the angular momentum of a particle .The angular momentum of a particle of mass m with respect to a chosen origin is given by

L = mvr sin θ

or more formally by the vector product

L = r × p

The direction is given by the right hand rule which would give L the direction out of the diagram. For an orbit, angular momentum is conserved, and this leads to one of Kepler's laws. For a circular orbit, L becomes

L = mvr

Angular momentum is perpendicular to the plane formed by the pair of position and linear momentum vectors or by the pair of position and velocity vector, depending upon the formula used. Besides, it is also perpendicular to each of operand vectors. However, the vector relation by itself does not tell which side of the plane formed by operands is the direction of torque