Questions: Conservation of Angular Momentum

Question 1

A figure skater spinning with arms extended pulls her arms in close to her body, halving her moment of inertia. What happens to her angular velocity?

• A. It halves
• B. It stays the same
• C. It doubles
• D. It quadruples

Answer: (C)

Angular momentum L = Iω is conserved because no external torque acts on the skater. If I decreases by half and L is constant, ω must double: L = I₁ω₁ = I₂ω₂ → ω₂ = (I₁/I₂)ω₁ = 2ω₁. The skater spins faster, but her total angular momentum is unchanged.

Question 2

When a figure skater pulls in her arms and spins faster, her angular momentum has increased.

• T. True
• F. False

Answer: False

This is a common misconception. Angular momentum is conserved — it does not change. What changes is how that fixed angular momentum is distributed: a smaller moment of inertia (arms in) requires a larger angular velocity to maintain the same L = Iω. The skater spins faster, but her total angular momentum is unchanged.

Question 3

What condition must be satisfied for the total angular momentum of a system to be conserved?

Model answer: The net external torque on the system must be zero.

This follows from Newton's second law for rotation: dL/dt = τ_net. If net external torque is zero, dL/dt = 0, so L is constant. Internal torques (forces between parts of the system) always come in equal and opposite pairs and cannot change the total angular momentum — only external torques can.