Angular Momentum Calculator
Calculate angular momentum for particles and rigid bodies in rotational motion
Calculator
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Rotation & Physics
Motion & Physics
Introduction
Angular momentum is the rotational equivalent of linear momentum and is conserved in systems with no external torques. It's a fundamental concept in physics that describes the quantity of rotation of an object.
This calculator helps you determine angular momentum for both point particles and rigid bodies, along with related parameters like moment of inertia and rotational kinetic energy.
How to Use
- Enter the mass of the particle (kg)
- Input the tangential velocity (m/s)
- Specify the distance from rotation axis (m)
- Click "Calculate" to get angular momentum and related parameters
- Review the results for your rotational motion analysis
Formula
L = Iω = mvr
L = Angular momentum (kg⋅m²/s)
I = Moment of inertia (kg⋅m²)
ω = Angular velocity (rad/s)
m = Mass (kg)
v = Tangential velocity (m/s)
r = Radius (m)
I = mr² (particle)
Moment of inertia for point particle
KE = ½Iω²
Rotational kinetic energy
Angular Momentum Formulas
Point Particle
L = m × v × r
Where L = angular momentum, m = mass, v = tangential velocity, r = radius
Rigid Body
L = I × ω
Where L = angular momentum, I = moment of inertia, ω = angular velocity
Related Formulas
Moment of Inertia (Particle): I = m × r²
Angular Velocity: ω = v ÷ r
Rotational Kinetic Energy: KE = ½ × I × ω²
Use Cases
Astrophysics
- Planetary orbital mechanics
- Stellar rotation and evolution
- Galaxy formation and dynamics
- Black hole angular momentum
Engineering
- Gyroscopes and navigation systems
- Turbine and rotor design
- Robotics and mechanical systems
- Satellite attitude control
Understanding Your Results
Angular Momentum (L)
The rotational equivalent of linear momentum, measured in kg⋅m²/s. Higher values indicate greater rotational motion.
Moment of Inertia (I)
Resistance to rotational acceleration, depends on mass distribution. Measured in kg⋅m².
Angular Velocity (ω)
Rate of rotation, measured in radians per second. Higher values mean faster spinning.
Rotational Kinetic Energy
Energy due to rotational motion, measured in joules. Important for understanding work and power in rotating systems.
Frequently Asked Questions
What is angular momentum conservation?
Angular momentum is conserved in isolated systems with no external torques. This means the total angular momentum remains constant, explaining phenomena like figure skaters spinning faster when pulling their arms in.
How is moment of inertia calculated?
For a point particle: I = mr². For rigid bodies, it depends on mass distribution and shape. Common formulas include I = ½mr² for disks and I = ⅔mr² for spheres.
What's the difference between linear and angular momentum?
Linear momentum (p = mv) describes straight-line motion, while angular momentum (L = Iω) describes rotational motion. Both are conserved quantities in their respective domains.
Conclusion
Angular momentum is a fundamental conserved quantity in physics that describes rotational motion. This calculator provides essential tools for analyzing rotating systems, from subatomic particles to galaxies and engineered mechanical systems.
Understanding angular momentum enables us to predict and control rotational behavior in countless applications, making it indispensable for physics, engineering, and astronomy.