Rotational Inertia Calculator

| Added in Physics

What is Rotational Inertia?

Rotational inertia (moment of inertia) is a measure of how resistant an object is to changes in its rotational motion. It is the rotational equivalent of mass in linear motion. The value depends on both the total mass and how that mass is distributed around the axis of rotation. Engineers and physicists use rotational inertia to predict how objects respond to applied torques.

How to Calculate Rotational Inertia

Here is the formula:

[I = \frac{L}{\omega}]

Where:

  • I is the rotational inertia (kg·m²).
  • L is the angular momentum (kg·m²/s).
  • ω is the angular velocity (rad/s).

Calculation Example

An object has an angular momentum of 30 kg·m²/s and an angular velocity of 15 rad/s.

[I = \frac{30}{15} = 2]

The rotational inertia is 2 kg·m².

Frequently Asked Questions

Rotational inertia, also called moment of inertia, measures how resistant an object is to changes in its rotational motion. It depends on both the mass of the object and how that mass is distributed relative to the axis of rotation. A larger moment of inertia means more torque is needed to change the rotation speed.

Angular momentum (L) equals rotational inertia (I) multiplied by angular velocity (omega). Rearranging gives I = L / omega. This means if you know how fast something is spinning and its angular momentum, you can find its rotational inertia.

Rotational inertia is measured in kilogram-meters squared (kg·m²) in SI units. This unit reflects that inertia depends on both mass (kg) and the square of the distance from the rotation axis (m²).

Mass farther from the rotation axis contributes more to rotational inertia than mass near the axis. A hollow cylinder has greater rotational inertia than a solid cylinder of the same mass because more of its mass is at a larger radius.

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