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 standard rotational inertia formulas for various shapes:

Common formulas include:

• Solid Sphere: \( I = \frac{2}{5}mr^2 \)
• Hollow Sphere: \( I = \frac{2}{3}mr^2 \)
• Solid Cylinder: \( I = \frac{1}{2}mr^2 \)
• Hollow Cylinder: \( I = mr^2 \)
• Rod (Center): \( I = \frac{1}{12}mL^2 \)
• Rod (End): \( I = \frac{1}{3}mL^2 \)

Explanation: Different shapes have different mass distributions, resulting in different rotational inertia values even with the same mass.

3. Importance of Rotational Inertia

Details: Rotational inertia is crucial in engineering, physics, and mechanical design. It affects how objects rotate, their stability, and the torque required to achieve angular acceleration.

4. Using the Calculator

Tips: Select the appropriate shape, enter mass in kg, radius in meters, and length when applicable. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between mass and rotational inertia?
A: Mass measures resistance to linear acceleration, while rotational inertia measures resistance to angular acceleration.

Q2: Why do different shapes have different formulas?
A: The mass distribution relative to the axis of rotation determines the rotational inertia value.

Q3: What units are used for rotational inertia?
A: Rotational inertia is measured in kg·m² (kilogram meter squared).

Q4: Can rotational inertia be negative?
A: No, rotational inertia is always a positive quantity since mass and distance squared are always positive.

Q5: How does axis location affect rotational inertia?
A: Rotational inertia increases as mass is distributed farther from the axis of rotation.