Question

The angular momentum of a system of particles is not conserved when

Answer 1

Angular momentum:

1. It is equal to the product of the angular velocity of the body or system and its moment of inertia with respect to the rotation axis.
2. It is a vector quantity which is a measure of the rotational momentum of a rotating body or system.
3. SI Unit of angular momentum $kg.m^2/s$

Mathematical expression for angular momentum:

1. Mathematically $∆\overrightarrow{L}=\stackrel{}{{\overrightarrow{{\rm T}}}_{ext}}.∆t$,
2. Or $\frac{∆\overrightarrow{L}}{∆t}={\overrightarrow{{\rm T}}}_{ext}$, Where $∆L$= change of angular momentum, ${\rm T}$= net torque, $∆t$ = time interval,
3. It is evident from the above-listed formula that the change in angular momentum is proportional to the average net torque and the time interval the torque is applied.
4. Hence, $\frac{∆\overrightarrow{L}}{∆t}={\overrightarrow{{\rm T}}}_{ext}$, When ${\overrightarrow{{\rm T}}}_{ext}\ne 0$, Then $\frac{∆\overrightarrow{L}}{∆t}\ne 0\Rightarrow \overrightarrow{L}\ne$constant, i.e. $\overrightarrow{L}$ is not conserved.

Thus, The angular momentum of a system of particles is not conserved when external torque acts on the system.