EngineeringEnergyGCSE
AQAEdexcelOCRAPIBCISCEICSECBSE

Kinetic Energy (Rotational) Calculator

Energy of a rotating object.

Use the free calculatorCheck the variablesOpen the advanced solver
Open Advanced Calculator
This is the free calculator preview. Advanced walkthroughs stay in the app.
Result
Ready
Kinetic Energy

Formula first

Overview

Rotational kinetic energy represents the energy an object possesses due to its rotation about a fixed axis. It is the angular equivalent of translational kinetic energy, where the moment of inertia replaces mass and angular velocity replaces linear speed.

Symbols

Variables

I = Moment of Inertia, = Angular Velocity, E = Kinetic Energy

Moment of Inertia
Angular Velocity
rad/s
Kinetic Energy

Apply it well

When To Use

When to use: Apply this equation when calculating the energy of spinning objects like flywheels, turbines, or rotating planets. It assumes the object is a rigid body and is rotating around a fixed axis or an axis passing through its center of mass.

Why it matters: This principle is critical for designing energy storage systems, understanding vehicle dynamics, and engineering industrial machinery. It explains how energy is stored in mechanical systems and why the distribution of mass affects how easily an object starts or stops spinning.

Avoid these traps

Common Mistakes

  • Using degrees/sec instead of rad/sec.
  • Convert units and scales before substituting, especially when the inputs mix kg·m², rad/s, J.
  • 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 heavy flywheel used for industrial energy storage has a moment of inertia of 5 kg·m² and is spinning at an angular velocity of 10 rad/s. Calculate the rotational kinetic energy stored in the flywheel.

Moment of Inertia5 kg·m²
Angular Velocity10 rad/s

Solve for:

Hint: Plug the values directly into the formula E = 0.5 ×I ×ω².

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Halliday, Resnick, Walker, Fundamentals of Physics
  2. Wikipedia: Rotational kinetic energy
  3. Bird, Stewart, Lightfoot, Transport Phenomena
  4. NIST Guide for the Use of the International System of Units (SI)
  5. IUPAC Gold Book: 'radian'
  6. Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics (10th ed.). John Wiley & Sons.
  7. Bird, R. B., Stewart, W. E., & Lightfoot, E. N. (2007). Transport Phenomena (2nd ed.). John Wiley & Sons.
  8. Halliday, Resnick, and Walker Fundamentals of Physics