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
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
Angular Momentum
Rotational equivalent of linear momentum
SI unit: kg⋅m²/s
Moment of Inertia
Resistance to rotational motion
Depends on mass distribution
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.