Suppose we have a disk of radius $r$ and mass $m$ travelling at velocity $v$. I want to calculate the instantaneous angular momentum with axis through the edge of the disc (on the circumference).
Angular momentum $= I \omega$. $I = \frac{1}{2}mr^2 + mr^2 = \frac{3}{2}mr^2$ by the parallel axis theorem. $\omega = \frac{v}{r}$. Therefore, angular momentum $= \frac{3mrv}{2}$.
Alternatively, angular momentum $=p\times r= m r \times v = mrv$.
Why do these two methods differ? Which, if any, are correct?
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