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 $\omega$ 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 ofthe above

Answer 1

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

Angular momentum is given by:

$\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}$

Since, the direction of $\overrightarrow{r}$ and $\overrightarrow{p}$ keep changing from point to point. Therefore, the direction of $\overrightarrow{L}$ also keeps changing but since the value of $|\overrightarrow{r}|$ and $|\overrightarrow{p}|$ is constant. The magnitude of $\overrightarrow{L}$ is constant.