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 points A is L_{A} which lies in the positive z direction and the angular momentum of M about point L_{B}. The correct statement for this system is :
Option: 1 L_{A} and L_{B} are both constant in magnitude and direction
 
Option: 2 L_{A} is constant, both in magnitude and direction
Option: 3 L_{B} is constant in direction with varying magnitude  
Option: 4 L_{B} is constant, both magnitude and direction

Answers (1)

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

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