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Moment of Inertia (Solid Disk) Calculator

Resistance of a disk to rotational acceleration.

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Moment of Inertia

Formula first

Overview

The moment of inertia for a solid disk represents its rotational resistance about a central axis perpendicular to its face. This property depends on both the total mass and the square of the distance of that mass from the axis of rotation.

Symbols

Variables

m = Mass, r = Radius, I = Moment of Inertia

Mass
kg
Radius
Moment of Inertia

Apply it well

When To Use

When to use: Apply this equation when calculating the rotational dynamics of uniform, rigid cylinders or flat circular plates. It assumes the mass is distributed evenly throughout the volume and the rotation occurs precisely through the geometric center.

Why it matters: This calculation is vital for mechanical engineers designing components like flywheels, gears, and pulleys where rotational stability and energy storage are key. It allows for the precise calculation of torque required to achieve specific angular accelerations in machinery.

Avoid these traps

Common Mistakes

  • Using diameter instead of radius.
  • Convert units and scales before substituting, especially when the inputs mix kg, m, kg·m².
  • Interpret the answer with its unit and context; a percentage, rate, ratio, and physical quantity do not mean the same thing.

One free problem

Practice Problem

A steel flywheel in an industrial engine is shaped like a solid disk with a mass of 50 kg and a radius of 0.4 meters. Calculate its moment of inertia about its central axis.

Mass50 kg
Radius0.4 m

Solve for:

Hint: Multiply half of the mass by the square of the radius.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Halliday, Resnick, Walker - Fundamentals of Physics
  2. Bird, Stewart, Lightfoot - Transport Phenomena
  3. Wikipedia: Moment of inertia
  4. IUPAC Gold Book (Compendium of Chemical Terminology), 'moment of inertia'
  5. NIST Guide for the Use of the International System of Units (SI) (NIST Special Publication 811)
  6. Halliday, Resnick, Walker, Fundamentals of Physics, 10th ed.
  7. Halliday, Resnick, Walker, Fundamentals of Physics, 11th Edition
  8. Beer, Johnston, Mazurek, Vector Mechanics for Engineers: Dynamics, 12th Edition