Conservation of Angular Momentum

The law of conservation of angular momentum states that the total angular momentum of an isolated system remains constant if no external torques act on the system.

Mathematical Expression

L⃗=r⃗×p⃗=constant\vec{L} = \vec{r} \times \vec{p} = constant
L=Iω=constantL = I\omega = constant
I1ω1=I2ω2I_1\omega_1 = I_2\omega_2

Key Concepts

  • Moment of inertia (I)
  • Angular velocity (ω)
  • Radius of rotation (r)
  • Torque (τ)

Applications

  • Figure skating spins
  • Planetary motion
  • Gyroscopes
  • Satellite stability
  • Binary star systems