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## Homework Statement

A uniform rod (M, L) is rotated about a point L/3 from its left end. Angular momentum about O

## Homework Equations

1) L=I(cm)w for purely rotating body

2) L(orbital)= M*v(cm)*perpendicular distance(r)

3) L(spin)= I*w

## The Attempt at a Solution

I got the correct answer in two ways- in the first one I wrote L= I about O*w. But isn't equation 1 applicable only when axis of rotation passes through COM? or is it applicable here because the body is not translating and thus there are no non-inertial forces on any point?

In the second method I wrote L=L(orbital)+L(spin), L(orbital) is m*v(cm)*distance between O and COM while L(spin) has to be taken as I about com*w...Why is L(spin) taken about an axis through COM even though the body isn't even rotating about that point? please reveal my conceptual flaws