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Angular Momentum of a Multi-Object System

APPHMC-Q1QKWX

Two bars of length $L$ and $\cfrac{L}{2}$ are connected at point $P$, where they are connected to a frictionless axle, as shown above. The total mass of both bars is $M$, and four smaller particles of mass $m$ are attached at the ends and centers of each bar.

If the system rotates clockwise with an angular velocity of magnitude $\omega$, what is the magnitude of the angular momentum of the system?

A

$(\cfrac{1}{36}M+\cfrac{25}{16}m)L^2 \omega$

B

$(\cfrac{2}{9}M+\cfrac{25}{16}m)L^2 \omega$

C

$(\cfrac{1}{4}M+\cfrac{25}{16}m)L^2\omega$

D

$(\cfrac{3}{2}M+\cfrac{5}{4}m)L^2 \omega$

E

$(\cfrac{2}{3}M+4m)L^2 \omega$