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In studying rotational dynamics of a rigid body, I can't seem to understand why you can solve the problem correctly only using certain points in a body and not all? Angular momentum and torque leads to correct answer only in some cases.

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up vote 2 down vote accepted

Firstly , definition of torque is $\vec{r}\times \vec{F}$ and angular momentum $\vec{r}\times \vec{p}$. And now w.r.t. your frame $\vec{F}$ & $\vec{p}$ & $\vec{r}$ are all relative . but newton's second law of rotation holds for all frames.

.Because all points are just frames and to maintain the distances in frame , you've to move with that frame , and as force and momentum both are relative to your frame , so will be torque and angular momentum , but the thing is they will all give the correct angular accelerations and angular velocities and linear velocities relative to them as Newton's laws can be made valid in all frames (by applying pseudo force in some) .

And answer in your book must be given in absolute terms , you can find correct answer by then applying gallilean relativity to your frame .

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