Rotational Kinetic Energy Calculator

What Is Rotational Kinetic Energy?

Rotational kinetic energy is the energy stored in a spinning object. Like linear kinetic energy depends on mass and speed, rotational energy depends on moment of inertia and angular velocity.

Rotational Kinetic Energy Formula

$$KE = \frac{1}{2} I \omega^2$$

$I$ is moment of inertia in kg·m² and $\omega$ is angular velocity in rad/s. For a solid disk or wheel, $I = MR^2$ where $M$ is mass and $R$ is radius.

Example: Spinning Wheel

A 1 kg wheel with radius 0.5 m has $I = 0.25$ kg·m². At 30 RPM ($\omega \approx 3.14$ rad/s), rotational kinetic energy is about 1.23 J.

Frequently Asked Questions

What units should I use?

Use kg·m² for moment of inertia and rad/s for angular velocity. Energy is in joules (J). Convert RPM to rad/s: ω = RPM × 2π / 60.

How is this different from linear kinetic energy?

Linear KE uses KE = ½mv² for straight-line motion. Rotational KE uses moment of inertia instead of mass and angular velocity instead of linear speed.

Can an object have both types of kinetic energy?

Yes. A rolling wheel has both translational KE (½mv²) and rotational KE (½Iω²). Total energy is the sum of both.

What is moment of inertia?

Moment of inertia measures resistance to angular acceleration. It depends on mass distribution relative to the rotation axis.

How do I convert RPM to rad/s?

Multiply RPM by 2π and divide by 60. For example, 30 RPM = 30 × 2π / 60 ≈ 3.1416 rad/s.

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Rotational Kinetic Energy Calculator

What Is Rotational Kinetic Energy?

Rotational Kinetic Energy Formula

Example: Spinning Wheel

Frequently Asked Questions

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