Moment of Inertia Calculator

Category: Physics
- April 04, 2025
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Calculate the moment of inertia for various shapes about different axes. The moment of inertia is a measure of an object's resistance to changes in its rotation rate.

Select Shape

Point Mass Parameters

Advanced Options

About Moment of Inertia

The moment of inertia, also called the mass moment of inertia or rotational inertia, is a measure of an object's resistance to changes in its rotational motion. It is the rotational analog of mass in linear motion.

Key Concepts
  • Moment of Inertia: Depends on both the mass of the object and how the mass is distributed relative to the axis of rotation.
  • Radius of Gyration: The distance from the axis of rotation at which the entire mass of the body could be concentrated without changing its moment of inertia.
  • Parallel Axis Theorem: Relates the moment of inertia about any axis to the moment of inertia about a parallel axis through the center of mass.
  • Perpendicular Axis Theorem: For a planar object, the moment of inertia about an axis perpendicular to the plane equals the sum of the moments of inertia about two perpendicular axes in the plane and through the same point.
Applications

Understanding moments of inertia is important in many fields:

  • Mechanical Engineering: Design of rotating machinery, balancing of wheels and turbines
  • Aerospace Engineering: Aircraft and spacecraft stability analysis
  • Structural Engineering: Analysis of beams and frameworks
  • Robotics: Motion planning and control of robotic arms
  • Sports Engineering: Design of equipment like baseball bats, tennis rackets, etc.
Units

The SI unit of moment of inertia is kilogram square meter (kg¡m²).

System Unit
SI kg¡m²
CGS g¡cm²
Imperial slug¡ft² or lb¡ft¡s²

What Is the Moment of Inertia Calculator?

This calculator helps you figure out the moment of inertia for different shapes based on their mass, dimensions, and axis of rotation. Moment of inertia is a physical quantity that indicates how much resistance an object has to changes in its rotation. It’s important in mechanical, structural, and physics-related applications.

Basic Formula:
I = m × r²

Where:

  • I is the moment of inertia
  • m is the mass of the object
  • r is the distance from the axis of rotation

Why Use This Calculator?

The moment of inertia changes depending on the shape of the object and its rotation. This calculator saves you time by doing the calculations for you. Whether you’re a student, teacher, engineer, or hobbyist, it makes analysis and planning for projects involving rotation or torque much easier.

Key Features

  • Choose from common shapes like rods, discs, cylinders, spheres, and more
  • Customise input values and units (e.g., mass in kg or g, length in m or cm)
  • Select different axes of rotation and see how the results change
  • Get extra insights like radius of gyration and density
  • View step-by-step calculation breakdowns for learning or verification
  • Offers advanced options like scientific notation and precision control

How to Use the Calculator

Just follow these simple steps to get your results:

  1. Select a Shape: Pick the physical shape that represents your object.
  2. Enter Parameters: Input values like mass, radius, or length based on the shape you selected.
  3. Set Axis of Rotation: Choose the relevant axis to calculate the correct moment of inertia.
  4. Adjust Settings (Optional): Select decimal precision or enable scientific notation if needed.
  5. Click "Calculate": Your results, along with a breakdown of calculations, will be shown instantly.

Who Can Benefit From This?

This tool is handy across various fields and activities:

  • Students: Learn and explore rotational mechanics through interactive examples.
  • Teachers: Demonstrate core physics concepts with clear visuals and numbers.
  • Engineers: Quickly calculate moments for structural or mechanical designs.
  • DIY Builders & Hobbyists: Plan projects that involve rotating parts like wheels or gears.

Frequently Asked Questions (FAQ)

What is the moment of inertia?
It measures how much an object resists rotating around an axis. Heavier and larger objects usually have higher moments of inertia.

Do I need to know the formula to use this tool?
No. The calculator automatically uses the correct formula based on the shape and inputs you provide.

Can I change units?
Yes. You can select from common units like kilograms or grams, meters or centimeters—whatever suits your data.

What if I want to see how the moment of inertia changes with a different axis?
Just select a new axis from the dropdown menu. The result will update to reflect that configuration.

Does this support complex shapes?
The calculator supports a wide range of standard shapes. For very irregular forms, custom modelling or software might be better suited.

Conclusion

The Moment of Inertia Calculator is a practical and educational tool. It provides quick, accurate results for rotational inertia calculations, helping users make informed choices in design, learning, or experimentation. It’s user-friendly, flexible, and designed to make physics more accessible.