20 lines
716 B
Markdown
20 lines
716 B
Markdown
For a point rotating around an origin:
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![[angular_momentum.jpg]]
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In the diagram the p vector is the momentum, i.e. the velocity times the mass.
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## Moment of inertia $I$ is rotational mass
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$$I = \sum mr^2$$It measures how strongly an object resists changes in its rotation
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* Large $I$ → harder to start, stop, or alter rotation
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- Small $I$ → easier to change rotation
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It depends on **mass distribution**, not just mass:
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Mass farther from the axis increases $I$ greatly.
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**Gyroscope connection:**
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$$L=I\omega$$
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Bigger $I$ → larger angular momentum at the same spin rate → harder to tilt or redirect.
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Can be thought of as: moment of inertia helps determine how “stubborn” a spinning object feels.
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