Question

A mass $M$ hangs on a massless rod of length $l$ which rotates at a constant angular frequency. The mass $M$ moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity $\omega$. The angular momentum of $M$ about point $A$ is $L _{ A }$ which lies in the positive $z$ direction and the angular momentum of $M$ about $B$ is $L _{ B }$. The correct statement for this system is :

• A. $L _{ A }$ and $L _{ B }$ are both constant in magnitude and direction
• B. $L _{ B }$ is constant in direction with varying magnitude
• C. $L _{ B }$ is constant, both in magnitude and direction
• D. $L _{ A }$ is constant, both in magnitude and direction

Answer 1

Answer: (D)

We know, $\overrightarrow{ L }= m (\overrightarrow{ r } \times \overrightarrow{ v })$
Now with respect to $A$, we always get direction of $\overrightarrow{ L }$ along +ve z-axis and also constant magnitude as mvr. But with respect to $B$, we get constant magnitude but continuously changing direction.