Angular Momentum Calculator

Calculate angular momentum using multiple formulas with real-time visualization. Perfect for students, teachers, and physics enthusiasts. Supports L = Iω, L = mvr, and kinetic energy relationships[citation:7][citation:10].

Angular Momentum (L)
0.00
kg·m²/s

Angular Momentum Visualization

Rotation Speed: 0 rad/s Simulated Mass: 1 kg
Adjust slider to visualize different angular velocities

Understanding Angular Momentum

Angular momentum is a fundamental concept in physics that describes the rotational motion of objects. Similar to linear momentum in straight-line motion, angular momentum is conserved in closed systems where no external torque is applied[citation:1][citation:9].

L = I × ω (for rigid bodies)
or
L = m × v × r (for point masses)

Angular momentum has two main types: spin angular momentum (rotation about an object's own center of mass) and orbital angular momentum (motion of the center of mass about an external point)[citation:1]. The direction of angular momentum follows the right-hand rule: curl your fingers in the direction of rotation, and your thumb points in the momentum direction.

Practical Examples & Applications

Example 1: Figure Skater Spin[citation:9]

A skater with moment of inertia 3.0 kg·m² spins at 2.0 rad/s. When they pull their arms in, reducing inertia to 1.0 kg·m², their angular velocity increases to 6.0 rad/s while conserving angular momentum (L = 6.0 kg·m²/s).

Example 2: Orbiting Satellite[citation:9]

A 1,500 kg satellite orbits at 7.5×10³ m/s with radius 6.5×10⁶ m. Using L = mvr, its angular momentum is 7.3×10¹³ kg·m²/s.

Real-World Applications:

  • Gyroscope stabilization systems
  • Planetary orbits and celestial mechanics
  • Ice skater spins and diving rotations
  • Bicycle wheel stability
  • Quantum mechanical systems

Conservation of Angular Momentum

The law of conservation of angular momentum states that when no external torque acts on a system, the total angular momentum remains constant[citation:1][citation:9]. This principle explains many physical phenomena:

If τ = 0, then ΔL = 0 (L remains constant)

This conservation law explains why:

  • Ice skaters spin faster when pulling arms inward
  • Planets maintain stable orbits around stars
  • Gyroscopes resist changes in orientation
  • Divers can control rotation speed by changing body position

The relationship between moment of inertia (I) and angular velocity (ω) means that as I decreases, ω must increase to maintain constant L, and vice versa[citation:9].

Frequently Asked Questions

What is the difference between angular momentum and linear momentum?
Angular momentum (L) describes rotational motion and depends on moment of inertia and angular velocity, while linear momentum (p) describes straight-line motion and depends on mass and linear velocity[citation:3]. Angular momentum is conserved when no external torque acts, while linear momentum is conserved when no external force acts.
What units are used for angular momentum?
The SI unit for angular momentum is kilogram meter squared per second (kg·m²/s)[citation:1][citation:3]. Other units include g·cm²/s and lb·ft²/s, but these require conversion for consistent calculations.
When should I use L = Iω vs L = mvr?
Use L = Iω for extended rigid bodies rotating about an axis (like a spinning wheel or Earth). Use L = mvr for point masses or particles moving in circular paths (like satellites or electrons in orbits)[citation:7].
How is angular momentum related to kinetic energy?
Rotational kinetic energy (KE) relates to angular momentum through L = √(2I·KE)[citation:10]. This formula is useful when you know the energy of rotation but not the angular velocity.
Junaid Ahmed
Junaid Ahmed
A high school teacher with ten years of experience and a lifelong love for physics. Holds a Bachelor of Engineering in computer science and enjoys making scientific ideas simple, clear, and engaging. Quiet by nature, but fully expressive when exploring motion, energy, and the wonders of the physical world.

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