1. What is Mass Moment of Inertia?

Mass moment of inertia (I) is a measure of an object's resistance to changes in its rotation rate. It depends on the object's mass and how that mass is distributed relative to the axis of rotation.

2. How Does the Calculator Work?

The calculator uses the fundamental equation:

Where:

• \( I \) — Mass moment of inertia (kg m²)
• \( m \) — Mass of the object (kg)
• \( r \) — Distance from the axis of rotation (m)

Explanation: The equation shows that moment of inertia increases with both mass and the square of the distance from the rotation axis.

3. Importance of Moment of Inertia

Details: Mass moment of inertia is crucial in mechanical engineering and physics for analyzing rotational dynamics, designing rotating machinery, and understanding angular momentum.

4. Using the Calculator

Tips: Enter mass in kilograms and radius in meters. Both values must be positive numbers. The calculator will compute the mass moment of inertia about the specified axis.

5. Frequently Asked Questions (FAQ)

Q1: How is this different from area moment of inertia?
A: Mass moment of inertia (I) relates to rotational kinetic energy of massive bodies, while area moment of inertia (J) relates to beam bending and torsion.

Q2: What if the mass isn't concentrated at a point?
A: For extended objects, integration is needed to account for mass distribution. This calculator assumes point mass.

Q3: What are typical values for common objects?
A: Values range widely: a small wheel might be 0.01 kg m², while large flywheels can be 100+ kg m².

Q4: How does radius affect the result?
A: Since radius is squared, doubling the distance quadruples the moment of inertia.

Q5: What are the units of measurement?
A: Standard SI units are kilogram meter squared (kg m²).