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Angular Momentum in Physics

Angular momentum is the quantity that keeps order when a body is spinning or moving sideways past a point. Unlike momentum it depends on where you stand, which is why the same motion can carry angular momentum about one origin and none about another. What makes it powerful is that it is conserved whenever no external torque acts, and that single fact explains a skater speeding up with arms pulled in, a collapsing star spinning faster as it shrinks, and a bicycle wheel staying upright when you lean it over. The blocks give the vector product it is built from, its particle and rigid body forms, the torque that changes it, and the slow circle a gyroscope traces.

Magnitude of the vector product of two vectors

Given

  • (rad)
Vector product from the components

Given

Angle between two vectors from their vector product

Given

Order in a vector product

Given

Torque written as a vector product

Given

  • (m)
  • (N)
Angular momentum of a particle

Given

  • (m)
  • (kg m/s)
Magnitude of the angular momentum of a particle from its speed

Given

  • (kg)
  • (m/s)
  • (m)
  • (rad)
Net torque and the rate of change of angular momentum

Given

Angular impulse and the change in angular momentum

Given

  • (N m)
  • (s)
Change in the angular momentum of a nonisolated system from a varying torque

Given

  • (s)
Angular momentum of a rigid body rotating about a fixed axis

Given

  • (kg m²)
  • (rad/s)
Angular speed of a rigid body from its angular momentum

Given

  • (kg m²/s)
  • (kg m²)
Conservation of angular momentum in an isolated system

Given

  • (kg m² and rad/s)
  • (kg m² and rad/s)
Precession rate of a spinning gyroscope

Given

  • (N m)
  • (kg m²/s)