Angular Momentum

Angular Momentum

Angular momentum is defined as the product of linear momentum of the particle and the perpendicular distance from the axis of rotation.

Expression for angular momentum:

Consider a particle of mass 'm' moving with velocity 'v' in a circular path orbit Z-axis (i.e, axis of rotation).

The Angular Momentum of the particle about the axis of rotation is given by:

L = r ✕ Ꝓ

(Ꝓ = mv)

Relation between Angular Momentum and Torque

Thus, Torque acting on a body is equal to the rate of change of angular momentum of the particle.

This equation also represents the  Rotational analogue of  Newton's Second law of motion.

Conservation of Angular Momentum

Consider a body of 'n' particles

then,

L= l₁ + l₂ + l₃ + . . . + lₙ

ⅆL / ⅆt = T

If External Torque = 0

then,

ⅆL / ⅆt = 0

∴L = 0

=>l₁ + l₂ + l₃ + . . . + lₙ = 0

▶ In a system of 2 particles:

l₁ = l₂                                      

as l = IѠ

∴ I₁Ѡ₁ = I₂Ѡ₂

Thus, Angular Momentum of a rigid body remains constant if net external acting on the body is zero.

This is known as the Law Of Conservation Of Angular Momentum.