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