When is angular momentum not parallel to angular velocity?

Developing some intuition about the direction of a rigid body's angular momentum, with the aid of some examples. We focus particularly on the case when angular momentum and angular velocity are in different directions, and discuss how to understand this scenario in terms of applied torque. The discussion is purely in terms of vector cross products, without referring to the inertia tensor.

The thumbnail shows the angular velocity and angular momentum of a rotating bar, with the small arrows represting the angular momentum contributions of particles at various positions throughout the bar.

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About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.

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