Angular Momentum Calculator

Calculate L for Point Mass, Rigid Body, and Orbital Motion

Input Parameters

Point Mass Formula:
L = m × v × r

What is Angular Momentum?

Angular momentum (L) is the rotational equivalent of linear momentum. It's conserved in isolated systems.

Formulas:

Point Mass: L = m × v × r

Rigid Body: L = I × ω

Orbital: L = m × r² × ω

Features

  • Point mass calculation
  • Rigid body calculation
  • Orbital motion calculation
  • Step-by-step solutions
  • Angular velocity calculation
  • Kinetic energy (rigid body)
  • Scientific notation support
  • Copy results
  • Quick examples

Conservation Law

Conservation:

In isolated systems, total angular momentum is conserved

Direction:

Angular momentum is a vector quantity

Units:

kg⋅m²/s or J⋅s

Common Examples

Figure Skater:

Pulls arms in to spin faster

Earth's Orbit:

L ≈ 2.7 × 10⁴⁰ kg⋅m²/s

Electron:

Intrinsic spin angular momentum

Gyroscope:

Maintains orientation due to L

Use Cases

  • Physics problems and homework
  • Rotational dynamics analysis
  • Orbital mechanics calculations
  • Engineering design
  • Astronomy and astrophysics
  • Quantum mechanics
  • Sports science
  • Mechanical systems

Applications

Real-World Applications:

Astronomy:

Planetary orbits, galaxy rotation

Engineering:

Gyroscopes, flywheels, turbines

Sports:

Diving, figure skating, gymnastics

Quantum:

Electron spin, atomic structure

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