Question

A conical pendulum consists of a simple pendulum moving in a horizontal circle as shown. C is the pivot, O the centre of the circle in which the pendulum bob moves and $\omega$ is the constant angular velocity of the bob. If $\overrightarrow{L}$ is the angular momentum about point C, then:

• A. $\overrightarrow{L}$ is constant
• B. only direction of $\overrightarrow{L}$ is constant
• C. only magnitude of $\overrightarrow{L}$ is constant
• D. none of the above.

Answer 1

The correct option is C only magnitude of $\overrightarrow{L}$ is constant

We have $\overrightarrow{L}=r\times m\overrightarrow{v}$. Here r is the distance between the bob and point C. This $\overrightarrow{r}$ keeps on changing during its motion. As the angular momentum $\overrightarrow{L}$ is always perpendicular to the the velocity vector $\overrightarrow{v}$ and radius vector $\overrightarrow{r}$ given by the right hand thumb rule, its direction keeps on changing as the radius vector changes. It however has a constant magnitude as the length and the velocity remains constant.