Angular Momentum Calculator

Calculate angular momentum for rotating objects and orbital motion with precise physics formulas

Calculate Angular Momentum

For objects rotating around their own axis (wheels, spinning tops, etc.)

Resistance to rotational motion

Rate of rotation

Angular Momentum Results

0.000000
kg⋅m2/s
0.000000
kg⋅m²/s (SI unit)

Formula used: L = I × ω

Calculation: L = 0.000000 kg⋅m² × 0.000000 rad/s = 0.000000 kg⋅m²/s

Example Calculations

Rotating Disk Example

Problem: A disk with moment of inertia 2 kg⋅m² rotates at 1 rad/s

Given: I = 2 kg⋅m², ω = 1 rad/s

Formula: L = I × ω

Solution: L = 2 × 1 = 2 kg⋅m²/s

Point Particle Example

Problem: A 3 kg particle moves at 2 m/s in a circle of radius 0.1 m

Given: m = 3 kg, v = 2 m/s, r = 0.1 m

Formula: L = m × v × r

Solution: L = 3 × 2 × 0.1 = 0.6 kg⋅m²/s

Key Concepts

L

Angular Momentum

Rotational equivalent of linear momentum

SI unit: kg⋅m²/s

I

Moment of Inertia

Resistance to rotational motion

Depends on mass distribution

ω

Angular Velocity

Rate of rotational motion

Unit: rad/s

Conservation of Angular Momentum

Law Statement

Angular momentum is conserved when no external torque acts on the system

Mathematical Expression

L = constant (when τ = 0)

Examples

  • • Ice skater spinning
  • • Planetary orbits
  • • Gyroscope stability

Key Formulas

Rotational Motion

L = I × ω

Orbital Motion

L = m × v × r

Point Particle Inertia

I = m × r²

Torque Relation

τ = dL/dt

Understanding Angular Momentum

What is Angular Momentum?

Angular momentum is the rotational equivalent of linear momentum. It measures the quantity of rotational motion an object possesses. Just as linear momentum is the product of mass and velocity, angular momentum involves rotational inertia and angular velocity.

Types of Angular Momentum

  • Spin Angular Momentum: Rotation about the object's own center of mass
  • Orbital Angular Momentum: Motion of the center of mass about an external axis

Physical Significance

  • Conserved quantity in the absence of external torque
  • Fundamental in rotational dynamics
  • Essential for understanding planetary motion
  • Key principle in quantum mechanics

Direction and Vector Nature

Angular momentum is a vector quantity. Its direction is perpendicular to the plane of rotation, following the right-hand rule: curl your fingers in the direction of rotation, and your thumb points in the direction of the angular momentum vector.

Real-World Applications

🌍 Planetary Motion

Planets conserve angular momentum as they orbit the Sun, moving faster when closer (perihelion) and slower when farther (aphelion).

⛸️ Figure Skating

Ice skaters spin faster when they pull their arms in, reducing moment of inertia while conserving angular momentum.

🚁 Helicopter Rotors

Helicopter main rotors create angular momentum that must be countered by a tail rotor to prevent the body from spinning.

🎯 Gyroscopes

Gyroscopes maintain their orientation due to conservation of angular momentum, making them useful for navigation systems.

🏀 Sports

Basketball players use angular momentum to control their rotation during aerial maneuvers, adjusting body position to land properly.

🛰️ Satellites

Satellites use reaction wheels to control their attitude by transferring angular momentum between the wheel and the satellite body.