Moment of Inertia Calculator
Moment of Inertia: - kg⋅m²
Angular Momentum (ω=1 rad/s): - kg⋅m²/s
Rotational Kinetic Energy (ω=1 rad/s): - J
Understanding Moment of Inertia
What is Moment of Inertia?
Moment of inertia is a measure of an object's resistance to rotational acceleration, analogous to mass in linear motion.
Common Formulas:
- Solid Cylinder: I = ½MR²
- Solid Sphere: I = ⅖MR²
- Thin Rod (about end): I = ⅓ML²
- Disk: I = ½MR²
- Ring: I = MR²
where:
- M = mass
- R = radius
- L = length
Advanced Rotational Dynamics
- Parallel Axis Theorem
- Perpendicular Axis Theorem
- Principal Axes of Inertia
- Inertia Tensor
- Angular Momentum Conservation
- Rotational Energy
- Gyroscopic Motion
- Precession and Nutation
- Moment of Inertia Coupling
- Rigid Body Dynamics
- Euler's Equations
- Rotational Stability
Applications and Analysis
Engineering
Machine design, balance
Aerospace
Spacecraft stability
Sports Science
Athletic performance
Robotics
Arm dynamics
Manufacturing
Industrial machinery
Astronomy
Celestial mechanics