Science
Angular momentum
Multiply moment of inertia about a fixed axis by angular velocity to find signed angular momentum; reversing rotation reverses its sign.
Calculators / Science / Rotational kinetic energy
Rotational kinetic energy calculator
Calculate rotational kinetic energy from moment of inertia and the square of angular velocity; rotation direction does not change the energy.
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Energy9J
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How to calculate
Calculate rotational kinetic energy from moment of inertia and the square of angular velocity; rotation direction does not change the energy.
Energy = I*w^2/2 J
Worked example
Moment of inertia (kg·m²): 2; Angular velocity (rad/s): 3.
Energy: 9 J.
Assumptions and limits
Calculate rotational kinetic energy from moment of inertia and the square of angular velocity; rotation direction does not change the energy. Assumes rotation about one fixed axis. Use the moment of inertia about that axis. Signed angular velocity sets the momentum direction.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Calculate rotational kinetic energy from moment of inertia and the square of angular velocity; rotation direction does not change the energy.
When this tool is useful
Energy = I*w^2/2 J
Understanding your inputs
| Input | What to enter |
|---|---|
| Moment of inertia (kg·m²) | Enter a number of at least 0 and no more than 1000000000000. |
| Angular velocity (rad/s) | Enter a number of at least -1000000000000 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
Calculate rotational kinetic energy from moment of inertia and the square of angular velocity; rotation direction does not change the energy. Assumes rotation about one fixed axis. Use the moment of inertia about that axis. Signed angular velocity sets the momentum direction.
How is the result calculated?
Energy = I*w^2/2 J