Moment of Inertia Calculator – Rotational Inertia
Calculate moment of inertia for different geometric shapes
Table of Contents
How to Use
- Select the shape of your object
- Enter the mass of the object in kilograms
- Enter the required dimensions (radius, length, width, height)
- Click calculate to see the moment of inertia
What is Moment of Inertia?
Moment of inertia (also called rotational inertia) is a measure of an object's resistance to changes in its rotation. It's the rotational equivalent of mass in linear motion.
The moment of inertia depends on both the mass of the object and how that mass is distributed relative to the axis of rotation. Objects with mass farther from the axis have higher moments of inertia.
Moment of Inertia Formulas
Different shapes have different moment of inertia formulas:
- Solid Sphere: I = (2/5)mr²
- Hollow Sphere: I = (2/3)mr²
- Solid Cylinder: I = (1/2)mr²
- Hollow Cylinder: I = mr²
- Rectangular Plate: I = (1/12)m(w² + h²)
- Rod (about center): I = (1/12)mL²
Where m is mass, r is radius, L is length, w is width, and h is height.
Applications
Moment of inertia calculations are essential in:
- Mechanical engineering and machine design
- Robotics and control systems
- Automotive engineering (flywheels, crankshafts)
- Aerospace engineering
- Sports equipment design
- Structural engineering
- Physics education and research
Frequently Asked Questions
- What is the difference between mass and moment of inertia?
- Mass is a measure of an object's resistance to linear acceleration, while moment of inertia is its resistance to rotational acceleration. Moment of inertia depends on both mass and how that mass is distributed.
- Why does a hollow sphere have a higher moment of inertia than a solid sphere?
- A hollow sphere has more mass concentrated farther from the rotation axis, which increases its moment of inertia. The farther mass is from the axis, the greater its contribution to rotational inertia.
- What are the units of moment of inertia?
- Moment of inertia is measured in kg⋅m² (kilogram-meter squared) in SI units. It can also be expressed in other unit systems like lb⋅ft² or g⋅cm².
- How does moment of inertia affect rotational motion?
- A higher moment of inertia means more torque is required to achieve the same angular acceleration. Objects with high moments of inertia are harder to start rotating and harder to stop once rotating.