Angular momentum about a point in translation
Physics Asked by newbie105 on February 28, 2021
Consider the following question which was asked in JEE Advanced 2016:
Consider the first option(which is the third option here)
In the video linked above, Tibees takes $L_{com}=L_1+L_2$ where $L_1$ & $L_2$ are the angular momenta caused by the rotation of the two discs about the line joining them.
My question is this- why is the angular momentum caused by translation of the system(since the system rotates about axis perpendicular to line joining them, which would provide a velocity $v$) not considered? It would give two additional angular momentum quantities
One Answer
What you are asking can be rephrased as: "why do we not include the angular momentum due to the center of mass motion of the rod?"
Keep in mind that the angular momentum has to be defined relative to an origin. Option A (sneakily) states that the origin to consider is not $O$ but the center of mass (COM). Therefore the distance from the origin to the COM is zero, and the angular momentum due to the COM motion $vec{L}_{rm COM}=m vec{r}_{rm COM} times vec{v}_{rm COM}=0$.
Answered by Andrew on February 28, 2021
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