Question

A conical pendulum consists of a simple pendulum moving in a horizontal circle as shown in the figure. $C$ 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 $\vec{L}$ is the angular momentum about point $C$, then

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

Answer 1

Answer: (C)

$\begin{array}{l}\overrightarrow{L}=m(\overrightarrow{CA}\times \vec{\nabla })\\ \overrightarrow{L}=m([\overrightarrow{CO}+\overrightarrow{OA}]\times \vec{v})\\ \overrightarrow{L}=mC\vec{O}\times \vec{v}+mOA\times \vec{v}\\ \overrightarrow{L}=m\overrightarrow{CO}\times \vec{v}+m|OA|v\hat{k}\end{array}$
Now, $\overrightarrow{CO}\times \vec{\nabla }$ will continously change its direction.
Thus $\overrightarrow{L}$ will change its direction at every instant but $|\overrightarrow{L}|=$ constant