# Angular Momentum

The turning momentum of a particle about the axis of rotation is called the angular momentum of the particle.

or

The moment of linear momentum of a body with respect to any axis of rotation is known as angular momentum. If  is the linear momentum of particle and  its position vector from the point of rotation (Fig. 6), then angular momentum

Fig. 6

Angular momentum is an axial vector, i.e., always directed perpendicular to the plane of rotation and along the axis of rotation.
• In case of circular motion,

= mvr sin φ

∴ L = mvr = mr2ω[as  and v = ]

or L = [as mr2 = I]

In vector form,
• From

i.e., the rate of change of angular momentum is equal to the net torque acting on the particle. [Rotational analogue of Newton’s second law]
• If a large torque acts on a particle for a small time, then “angular impulse” of torque is given by

or Angular impulse,

∴ Angular impulse = Change in angular momentum
• The angular momentum of a system of particles is equal to the vector sum of angular momentum of each particle, i.e., .