notes/Angular Momentum.md

For a point rotating around an origin: ! In the diagram the p vector is the momentum, i.e. the velocity times the mass.

Moment of inertia I is rotational mass

I = \sum mr^2

• Large I → harder to start, stop, or alter rotation

• Small I → easier to change rotation

It depends on mass distribution, not just mass: Mass farther from the axis increases I greatly.

Gyroscope connection:

L=I\omega

Bigger I → larger angular momentum at the same spin rate → harder to tilt or redirect. Can be thought of as: moment of inertia helps determine how “stubborn” a spinning object feels.

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