[Leejohnston]

## Angular Momentum — Why Orbits Stay Stable

### 1. The Equation

Angular momentum:

L = mvr

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### 2. What Each Symbol Means

- L = angular momentum
- m = mass
- v = velocity
- r = distance from rotation axis

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### 3. What the Equation Is Telling Us

Angular momentum is conserved unless acted on by an external torque.

When radius decreases, speed must increase.

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### 4. Where It Comes From (Intuition)

Rotational motion follows the same conservation logic as linear motion.

Nothing is lost — it shifts between speed and distance.

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### 5. Worked Example

A satellite moves closer to Earth →
it speeds up to conserve angular momentum.

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### 6. Real-World Applications

- Planetary orbits
- Ice skaters spinning
- Gyroscopes
- Accretion disks

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### 7. Common Misconceptions

- Objects slow naturally in orbit → false
- Rotation needs constant force → false
- Angular momentum depends on gravity → false

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### Try It Yourself

Why does an ice skater spin faster when pulling in their arms?