# Under what conditions does L=Iw hold?

So, that is the question: Under what conditions does L=Iw hold? Where L,I,w are all scalars.
Some specifics perhaps:
1) Supose a fixed axis of rotation, with accel, does is hold?
2) Suppose de axis of rot is not a ppal axis
3) Suppose there is fixed axis of rot, but I choose neither x nor y nor z to be in that direction, I'll have to use the I tensor, right?

Anyway this are just suggestions.
Thanks a lot.

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For any FIXED axis, you can find a scalar I that satisfies L=Iw. It's only when the axis of rotation changes, such as in tumbling or if torque is applied, that tensor qualities of moment of inertia become important.

L=I*ω should hold in zero gravity on the International Space Station. See video of rotating book flipping axis of rotation in the video In this video, neither I nor ω is constant, although the product is.

In this video clip, Pettit demonstrates stable and unstable modes for solid body rotation on the ISS. Using a hard cover textbook, he demonstrates that it will rotate stably about the longest and shortest axis, which represent the maximum and minimum movements of Inertia. Trying to rotate the book around an intermediate axis results in an unstable rotation in which the book appears to flip-flop while it rotates.

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