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.