What is Angular Momentum?
Angular momentum measures how much rotational motion an object has and how hard it would be to stop it from spinning. It depends on both how the mass is distributed (moment of inertia) and how fast the object rotates.
Angular momentum is the rotational analogue of linear momentum: L = Iω, where I is the moment of inertia and ω is the angular velocity, measured in kg·m²/s.
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Step-by-step worked examples
A flywheel has a moment of inertia of 2 kg·m² and spins at 10 rad/s. Find its angular momentum.
L = Iω L = 2 × 10 L = 20 kg·m²/s
A figure skater has I = 4 kg·m² while spinning at ω = 3 rad/s. Find L.
L = Iω L = 4 × 3 L = 12 kg·m²/s
The same skater pulls her arms in, dropping I from 6 kg·m² to 2 kg·m² while spinning at ω = 2 rad/s. If angular momentum is conserved, find her new angular velocity.
L is conserved: L = I₁ω₁ L = 6 × 2 = 12 kg·m²/s ω₂ = L / I₂ = 12 / 2 ω₂ = 6 rad/s
Flashcards
Quick quiz
Q1.A wheel has I = 3 kg·m² and ω = 5 rad/s. What is L?
Q2.What is the SI unit of angular momentum?
Q3.A skater spinning with arms out has a larger I than with arms in. If L is conserved, arms in means:
Q4.Angular momentum is the rotational analogue of:
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Common mistakes
Angular momentum and torque are the same thing. — Correct: Torque is the rate of change of angular momentum (τ = dL/dt), not L itself.
Angular velocity ω must be in degrees per second. — Correct: ω must be in radians per second for L = Iω to give correct SI units.
Angular momentum is only for spinning objects. — Correct: Even an object moving in a straight line has angular momentum about a point not on its path (L = r×p).
Reducing moment of inertia always slows rotation. — Correct: By conservation of L, reducing I actually increases ω — the object spins faster.
FAQ
What is the formula for angular momentum?
L = Iω, where I is the moment of inertia (kg·m²) and ω is the angular velocity (rad/s), giving L in kg·m²/s.
What is angular momentum in physics?
It's the rotational equivalent of linear momentum — a measure of how much an object resists a change in its spin.
How do you calculate angular momentum for a skater?
Multiply moment of inertia by angular velocity: L = Iω. Since L is conserved, pulling arms in (lower I) raises ω.
Is angular momentum always conserved?
Yes, when no external torque acts on the system — this is the law of conservation of angular momentum.