A small mass $m$ is attached to a massless string whose other end is fixed at $P$ as shown in the figure.…
A small mass $m$ is attached to a massless string whose other end is fixed at $P$ as shown in the figure. The mass is undergoing circular motion in the $x-y$ plane with centre at $O$ and constant angular speed $\omega$. If the angular momentum of the system, calculated about $O$ and $P$ are denoted by $\vec{L}_{O}$ and $\vec{L}_{P}$ respectively, then
$\vec{L}_{O}$ and $\vec{L}_{P}$ do not vary with time
$\vec{L}_{O}$ varies with time while $\vec{L}_{P}$ remains constant
$\vec{L}_{O}$ remains constant while $\vec{L}_{P}$ varies with time
$\vec{L}_{O}$ and $\vec{L}_{P}$ both vary with time
Solution
For all locations of $\mathrm{m}$ the angular momentum of the mass $m$ about $O$ i.e., $L_{o}$ is $m r^{2} \omega$ and is directed toward $+z$ direction. The angular momentum of mass $m$ about $P$ i.e., $L_{p}$ is $m v l$ and is directed for the given location of $m$ as shown in the figure. For different location of $m$, the direction of $\vec{L}_{P}$ remains changing.
