AP Physics 1: Angular Momentum

$ap-physics-1-angular-momentum, A high-tech physics illustration of a spinning gyroscope with a vertical vector arrow representing Angular Momentum ($L$), showing the conservation equation $L_{initial} = L_{final}$.$

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AP Physics 1 Unit 7: Angular Momentum

Topic 7.3 (10–15% exam weight): Just as linear momentum ( $p= mv$ ) is hard to stop, Angular Momentum ( $L$ ) resists changes in rotation. Governs ice skaters, gyroscopes, and planetary orbits.

1. Angular Momentum ( $L = I\omega$ )

$L = I\omega$

Rigid body: kg·m²/s | Direction: Right-hand rule

2. Conservation Law

Net external torque = zero → Angular momentum conserved:

$\tau_{ext} = 0 \quad \Rightarrow \quad L_i = L_f$

$I_1\omega_1 = I_2\omega_2$

Ice skater arms out (slow ω, high I) vs arms in (fast ω, low I).

Ice Skater Effect: $I\downarrow \Rightarrow \omega\uparrow$ (L constant).

Why Speed Up?

Arms in → Mass closer to axis → $I\downarrow$
$L=I\omega$ conserved → $\omega\uparrow$
Muscles do work → $K\uparrow$

⚠️ Exam Trap: $L$ conserved (no $\tau_{ext}$ ), but $K$ changes (work done). Ice skater spins faster AND gains rotational KE.

3. Particle Angular Momentum ( $L = mvr_\perp$ )

Straight-line motion has $L$ relative to pivot:

$L = m v r_\perp = m v r \sin\theta$

Bullet hitting rod, orbiting planets

Particle mass m, velocity v, perpendicular distance r_perp from pivot.

$L=mvr_\perp$ : Straight line motion still has angular momentum.

4. Angular Impulse

$\Delta L = \tau_{net} \Delta t$

Torque × time = change in angular momentum

5. Quick AP Practice

📚 AP Practice Problems

1. Ice skater pulls arms in. $L$ ? $K$ ?

Answer

$L$ constant, $K\uparrow$ . No $\tau_{ext}$ , so $L$ conserved. Muscles do work → $K=\frac{L^2}{2I}\uparrow$ .

2. 2 kg ball at 3 m/s, $r_\perp$ =4 m. $L$ ?

Answer

$L = mvr_\perp = (2)(3)(4) = 24 \, \text{kg·m}^2\text{/s}$

3. Bullet hits rod end ( $I\uparrow$ ). Final $\omega$ ?

Answer

$L_i = L_f \Rightarrow mvr = I_{final}\omega_f \Rightarrow \omega_f = \frac{mvr}{I_{final}}$

🔗 Related AP Physics Resources

🎉 Unit 7 COMPLETE!

You mastered torque, rotational motion, and angular momentum conservation. Next: the NEW Unit 8 Fluids (2025+).

Next Unit: Fluids (Unit 8)->Density & Pressure →