Angular Momentum & Moment of Inertia Calculator
### Physics & Classical Mechanics: Conservation of Angular Momentum 1. **The Law of Conservation of Angular Momentum**: In the absence of an external net torque, total angular momentum remains.
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📐 Formula
💡 Practical Example
For example, evaluating a \(15.0\text{ kg solid steel flywheel disk}\) with radius \ spinning at \(1,200\text{ RPM}\)): Moment of inertia is \(0.5)^2 = \mathbf{1.875\text{ kg}\cdot\text{m}^2}\). Angular Momentum is \}}\), storing \(\mathbf{14.80\text{ kJ (14,804 Joules)}}\) of rotational energy with an outer rim speed of \}\).
📖 About Angular Momentum & Moment of Inertia Calculator
Physics & Classical Mechanics: Conservation of Angular Momentum
- The Law of Conservation of Angular Momentum: In the absence of an external net torque, total angular momentum remains strictly constant: .
- The Figure Skater Effect: When an ice skater pulls their arms inward, their radius r decreases, slashing their moment of inertia I; to conserve L, their angular spin speed ω accelerates dramatically.
How to Use This Calculator
Enter your Rotating Body Geometry — choose from Solid Cylinder / Disk / Flywheel (I = 1/2 m r²), Point Mass / Orbiting Particle (I = m r²), Solid Sphere / Planet (I = 2/5 m r²), Object Mass (m [kg]) (e.g. 15 (15 kg flywheel / satellite)), Radius or Length (r [Meters]) (e.g. 0.5 (0.5 meters = 50 cm)), Rotational Velocity Input Unit — choose from Revolutions Per Minute (RPM), Radians per Second (rad / s), and Rotational Speed (RPM or rad / s) (e.g. 1200 (1,200 RPM)). Verify your units match the formula standard (SI vs imperial) before entering values.
The Formula
Rotational Dynamics \& Angular Momentum equations:
Angular Momentum: L = I × ω (kg·m^2/s or J·s)
Solid Cylinder Inertia: I = (1) / (2) m r^2, Solid Sphere: I = (2) / (5) m r^2, Point Mass: I = m r^2
Angular Velocity: ω = (2 π × RPM) / (60) (rad/s)
Rotational Kinetic Energy: E_rot = (1) / (2) I ω^2 (Joules)
Tangential Rim Velocity: v_tan = ω × r (m/s)
Worked Example
For example, evaluating a 15.0 kg solid steel flywheel disk with radius \ spinning at 1,200 RPM): Moment of inertia is 0.5)^2 = 1.875 kg·m^
- Angular Momentum is \, storing 14.80 kJ (14,804 Joules) of rotational energy with an outer rim speed of \.
Understanding Your Result
Scientific calculations require careful attention to significant figures and units. Your result is only as precise as your least precise input — expressing the result with more significant figures than the inputs implies false precision. For laboratory or regulatory work, verify which measurement standard applies (SI, ASTM, ISO) and whether temperature, pressure, or concentration conditions affect the formula. Cross-reference results against published reference values for your specific material or compound.
💡 Methodological Standards & Calculation Accuracy
- All calculations are performed client-side in your browser using verified, standards-compliant mathematical algorithms.
- Results are provided for educational and informational analysis; verify critical applications with certified domain specialists.
- Ensure input values are entered in consistent units matching the selector options to guarantee accurate outputs.
- Periodic recalibration is recommended whenever baseline assumptions, operating parameters, or external conditions change.
Results are for informational and educational purposes only. Always verify critical decisions with a qualified professional.