Question

A conical pendulum consists of a simple pendulum moving in a horizontal circle as shown in the figure. C is the pivot, O is 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 of the above

Answer 1

Answer: (C)

only magnitude of $\overrightarrow{L}$ is constant

$\overrightarrow{L}=m(\overrightarrow{CA}\times \overrightarrow{v})$

$\overrightarrow{L}=m\left(\right[\overrightarrow{CO}+\overrightarrow{OA}]\times \overrightarrow{v})$

$\overrightarrow{L}=m\overrightarrow{CO}\times \overrightarrow{v}+m\overrightarrow{OA}\times \overrightarrow{v}$

$\overrightarrow{L}=m\overrightarrow{CO}\times \overrightarrow{v}+m|OA|v\hat{k}$

Now, $\overrightarrow{CO}\times \overrightarrow{v}$ will continously change its direction. Thus $\overrightarrow{L}$ will change its direction at every instant but $|\overrightarrow{L}|=constant$