1. What is Rotational Inertia?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotation rate. It depends on the mass distribution relative to the axis of rotation.

2. How Does the Calculator Work?

The calculator uses the rotational inertia formula:

Where:

• \( I \) — Moment of inertia (kg·m²)
• \( m_i \) — Mass of each particle (kg)
• \( r_i \) — Distance from axis of rotation (m)

Explanation: The formula calculates the sum of each mass multiplied by the square of its distance from the rotation axis.

3. Importance of Moment of Inertia

Details: Moment of inertia is crucial in rotational dynamics, affecting how objects rotate under applied torques. It's essential in engineering, physics, and mechanical design applications.

4. Using the Calculator

Tips: Enter masses in kilograms and distances in meters as comma-separated values. Both lists must have the same number of values and all values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for mass and distance?
A: Use kilograms for mass and meters for distance to get moment of inertia in kg·m².

Q2: Can I calculate inertia for continuous objects?
A: This calculator is for discrete point masses. For continuous objects, integration is required using specific formulas for different shapes.

Q3: How does mass distribution affect rotational inertia?
A: Mass farther from the axis contributes more to rotational inertia due to the r² term in the formula.

Q4: What's the difference between mass and moment of inertia?
A: Mass measures resistance to linear acceleration, while moment of inertia measures resistance to angular acceleration.

Q5: Can moment of inertia be negative?
A: No, moment of inertia is always positive since it involves squared distances and positive masses.