Question

Under what circumstances is angular momentum constant? Give an example of a situation in which the x component of angular momentum is constant, but the y component isn’t.

Short answer

The x component of the angular momentum is zero.

Step-by-step solution

Definition of Angular Momentum

The rotating inertia of an object or system of objects in motion about an axis that may or may not pass through the object or system is described by angular momentum.

Derivation of Angular Momentum

The net torque ($\tau$) exerted to a particle about a given place equals the rate of change of its angular momentum at that location.

It is given by formula:

$\tau =\frac{dL}{dt}$ …… (1)

If the external torque is not applied,$\tau =0$,

Then equation (1), is written as

$$\begin{gathered} \frac{dL}{dt}=0 \\ dL=0 \\ {L}_f=L_i \end{gathered}$$

Final angular momentum $\left(L_f\right)$is equal to the initial angular momentum $\left(L_i\right)L\to$

Constant

If the net torque acting on the particle is zero, the total angular momentum of the rotating object remains constant.

Step 3: The situation in which the x component of angular momentum is constant is-

This is fixed at one end and moves in a plane of the paper when a ball moves in a circular manner. There will be a torque acting in the vertical direction due to gravitational and centripetal force.

As a result, the angular momentum component does not remain constant. The direction isn't affected by any horizontal torque. As a result, the angular momentum component has no value.