Home
Back
Moment of Inertia Formulas:
For a rod: I = (1/12) M L²
For a solid sphere: I = (2/5) M R²
For a hollow cylinder: I = M R²
| From: | To: |
Moment of Inertia (I) is a physical quantity that represents an object's resistance to changes in its rotation. It depends on the mass distribution relative to the axis of rotation and is measured in kg·m².
The calculator uses standard formulas for different shapes:
For a rod: I = (1/12) M L²
For a solid sphere: I = (2/5) M R²
For a hollow cylinder: I = M R²
Where:
Explanation: Different shapes have different mass distributions, which affects their resistance to rotational motion.
Details: Calculating moment of inertia is crucial in mechanical engineering, physics, and various applications involving rotational motion, such as designing rotating machinery, analyzing vehicle dynamics, and understanding celestial mechanics.
Tips: Select the shape, enter mass in kilograms, and length/radius in meters. All values must be positive numbers.
Q1: Why does shape affect moment of inertia?
A: Different shapes distribute mass differently relative to the axis of rotation, which changes how much torque is needed to achieve angular acceleration.
Q2: What's the difference between moment of inertia and mass?
A: Mass measures resistance to linear acceleration, while moment of inertia measures resistance to angular acceleration.
Q3: Can I calculate moment of inertia for complex shapes?
A: Complex shapes often require integration or can be broken down into simpler components whose moments of inertia are summed.
Q4: How does axis position affect moment of inertia?
A: Moment of inertia increases when mass is distributed farther from the axis of rotation, following the parallel axis theorem.
Q5: Are these formulas for specific axes?
A: Yes, these formulas assume rotation about specific axes (center of mass for rod and sphere, central axis for cylinder).