AP Physics 1 · Unit 6: Energy & Momentum of Rotating Systems ·  Lesson 6.4

Conservation of Angular Momentum

The figure skater revealed — when net external torque is zero, total angular momentum never changes, no matter how the system rearranges itself  ·  Approx. 3–4 class days

StarringL_i = L_fI_1*omega_1 = I_2*omega_2
Unit 6: Energy & Momentum of Rotating Systems

Use this as a quick reference for L_i = L_f, the zero-torque rule, nonrigid systems, system selection, and Newton's Third Law in rotation.

Principles of Conservation of Angular Momentum infographic

🧭 Plot Summary

This is the payoff of Lesson 6.3. You now know that angular momentum L = Iω can be changed by an angular impulse. This lesson asks: what happens when nothing outside the system applies a torque? The answer is the conservation of angular momentum — L_total stays constant forever, even as the system rearranges its mass, changes shape, or has internal collisions.

The condition is simple: net external torque = 0. When that holds, the total angular momentum of the system cannot change. For a nonrigid system that changes shape (like a skater pulling arms in), I decreases so ω must increase to keep L = Iω constant. For a collision between a spinning and a stationary object, L is shared between them after contact — but the total remains unchanged.

Three problem types in this lesson

Shape changeSame object, I changes. Skater, diver, spinning stool. Use I_1*omega_1 = I_2*omega_2.
Rotational collisionSpinning object contacts stationary one. Angular momentum shared. L_i = L_f with two-part final I.
System selectionChoose your system so net external torque = 0. Internal torques cancel by Newton's Third Law.

What you will do in this lesson

  • State the conservation law: L_total = constant when net external torque = 0.
  • Apply L_i = L_f in the form I_1*omega_1 = I_2*omega_2 for shape-changing systems.
  • Define the system strategically so that internal torques cancel and external torques are zero.
  • Apply Newton's Third Law in rotation: equal and opposite angular impulses between interacting objects.
  • Solve collision-style angular momentum problems where spinning and stationary objects interact.
  • Justify conservation claims with evidence from physical representations and laws.

Why it matters

Conservation of angular momentum is one of the most fundamental laws in physics — it holds from spinning electrons to orbiting galaxies. On the AP exam it appears as FRQs requiring before/after diagrams, an explicit statement of the condition for conservation, and algebraic solutions. It also appears qualitatively: "what happens to omega if I is halved?" Answer: omega doubles.

✅ Self-Check Before You Roll On

Check off each item as you get there. These are not grades — they are your own signal.