Angular Momentum
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 6 practice questions.
Angular momentum is the rotational version of momentum. For a spinning object, L = Iω. For a small object moving past an axis, L = mvr, where r is its distance of closest approach to the axis. Always pick the axis first: L depends on it.
1. Two ways to have angular momentum
2. Direction
Angular momentum is a vector. Curl the fingers of your right hand in the direction of rotation; your thumb points along L. In most AP problems, you just call counterclockwise + and clockwise −.
Angular momenta in the same rotational sense add; opposite senses subtract. 8 kg·m²/s clockwise and 3 kg·m²/s counterclockwise give 5 kg·m²/s clockwise.
3. Example, then try it
A wheel with I = 0.50 kg·m² spins at 10 rad/s. What is its angular momentum?
L = Iω = (0.50)(10) = 5.0 kg·m²/s.
A 60 kg skater glides in a straight line at 4.0 m/s, passing 2.0 m from a post at her closest approach. A merry-go-round (I = 400 kg·m²) spins at 1.2 rad/s. Compare their angular momenta about their axes.
Skater about the post: L = mvr = (60)(4.0)(2.0) = 480 kg·m²/s.
Merry-go-round: L = Iω = (400)(1.2) = 480 kg·m²/s.
Compare: they’re equal, even though the skater isn’t moving in a circle.
Answer: both are 480 kg·m²/s. (If she grabs the post, that angular momentum turns into spinning around it.)
4. Common mistakes
A puck slides across frictionless ice in a straight line at constant speed, on a path that misses point P. What happens to its angular momentum about P as it slides past?
L = mvr, where r is the distance of closest approach to P. The mass, speed, and closest-approach distance never change, so L stays constant.
Ready to practice?
6 questions on Angular Momentum, each with a hint and an explanation for every wrong answer.