Angular Momentum

Angular momentum is the rotational analogue of linear momentum in Newtonian physics.

The angular momentum $ \hat L $ of a solid body is the product of its moment of inertia I and angular velocity $ \hat \omega $.

$ \hat L=I \hat \omega $

In a closed system angular momentum is conserved. Curiously, angular momentum is a vector quantity, and points in the same direction as the angular velocity of the object.

The angular momentum of a system of N particles is just the vector summation of all of its constituents.

$ \hat L =  I_1 \omega_1 +  I_2 \omega_2 +... + I_N \omega_N = \Sigma_{i=1}^N I_i \omega_i $

The angular momentum $ \hat L $ of a point particle of mass m, moving with velocity $ \hat v $, at a distance $ \hat r $, from some reference point is:

$ \hat L = m \hat r \times \hat v $

where the $ \times $ is the vector cross product. The direction of the vector is given by the right hand rule – by holding the fingers in the direction of $ \hat r $ and sweeping them towards $ \hat v $, the thumb dictates the direction of the resultant vector.

Study Astronomy Online at Swinburne University
All material is © Swinburne University of Technology except where indicated.