Angular Momentum Calculator - Rotational Momentum

This physics calculator helps you calculate angular momentum using various methods. Angular momentum is the rotational equivalent of linear momentum and is conserved in isolated systems.

Angular Momentum Definition

• Angular Momentum: Rotational momentum of an object
• SI Unit: kg⋅m²/s
• Formula: L = Iω
• Conservation: Conserved in isolated systems

Angular Momentum Formulas

• Basic: L = Iω
• Particle: L = mvr
• Rigid Body: L = mr²ω
• Change: ΔL = τΔt
• Kinetic Energy: E = ½Iω²
• Impulse: J = τΔt

Applications

• Mechanics: Rotational motion and conservation
• Astronomy: Planetary and stellar rotation
• Engineering: Gyroscopes and flywheels
• Sports: Figure skating and diving
• Quantum Physics: Electron spin and atomic orbitals
• Robotics: Balance and stability control

Important Notes

• Angular momentum is a vector quantity
• Direction follows right-hand rule
• Conserved in isolated systems
• Changes only with external torque
• Related to rotational kinetic energy

Conservation of Angular Momentum

• Isolated System: No external torques
• Conservation Law: L = constant
• Applications: Ice skater effect, planetary orbits
• Examples: Spinning top, rotating planet
• Implications: Changes in I affect ω

Angular Momentum Types

• Orbital: Due to motion around a point
• Spin: Due to rotation about own axis
• Total: Sum of orbital and spin
• Intrinsic: Quantum mechanical property
• Extrinsic: Due to external motion

Common Examples

• Spinning Top: L = Iω (stable rotation)
• Planet: L = mr²ω (orbital + spin)
• Gyroscope: L = Iω (precession)
• Figure Skater: L = constant (I changes)
• Electron: L = ħ√(l(l+1)) (quantized)

Angular Momentum Relationships

• Torque: τ = dL/dt
• Energy: E = L²/(2I)
• Power: P = τω
• Impulse: J = ΔL
• Momentum: p = L/r

Angular Momentum Units

• SI: kg⋅m²/s
• CGS: g⋅cm²/s
• Imperial: lb⋅ft²/s
• Atomic: ħ (Planck's constant)
• Astronomical: M☉⋅AU²/year

Angular Momentum Measurement

• Gyroscope: Precession measurement
• Optical Methods: Doppler effect
• Magnetic Methods: NMR spectroscopy
• Mechanical: Torsion pendulum
• Quantum: Stern-Gerlach experiment