## Statement of the Law of **Conservation of Angular Momentum**

The **Law of** **Conservation of Angular Momentum** states that angular momentum remains constant if the net external torque applied on a system is zero.

So, when net external torque is zero on a body, then the net change in the angular momentum of the body is zero.

## Derivation of the expression for the Law of **Conservation of Angular Momentum**

This law can be mathematically derived very easily using one of the Torque equations,

We know that Torque = T = **I α** ……………(1)

[ Torque is the product of Moment of Inertia (I) and **α** (alpha, which is angular acceleration) ]

Expanding the equation, we get

T = I (ω2-ω1)/t

[ here **α** = angular acceleration

= time rate of change of angular velocity

= (ω2-ω1)/t

where ω2 and ω1 are final and initial angular velocities and t is the time gap]

or, **T t = I (ω2-ω1) ……………………(2)**

**Torque is presented with the help of symbol τ (tao) or T.

From equation (2):

when, T = 0 (i.e., net **torque** is zero), then from the above equation we get,

I (ω2-ω1) = 0

i.e., **I ω2=I ω1 ………….. (3)**

Iω2 represents final angular momentum and Iω1 represents initial angular momentum.

So, this shows that when net torque on a body is zero, then the angular momentum of the body remains unchanged. Thus we can do the derivation of the expression of the law.

## conclusion

Angular momentum remains constant if the net external torque applied on a system is zero. We can derive its expression and prove the law mathematically with the help of a torque equation.