Rotational kinetic energy
Energy for the stated reference and ideal model.
Physics · Mechanics · Motion & Energy
Rotational kinetic energy calculator
Find rotational energy, moment of inertia or angular-speed magnitude. Supply the moment of inertia about the actual axis of rotation.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Mass moment of inertia
Mass moment of inertia about the specified rotation axis.
Angular velocity
Signed input in energy mode; nonnegative magnitude in the inverse speed mode.
Relation and numerical substitution
K = ½ × I × ω²—
Rigid body, fixed axis, I > 0; energy ≥ 0; inverse ω is a magnitude.
01Formulas and symbols
Formulas used
K
K = ½ × I × ω²Energy for the stated reference and ideal model.I
I = 2 × K / ω²Mass moment of inertia about the specified rotation axis.ω
ω = √(2 × K / I)Signed input in energy mode; nonnegative magnitude in the inverse speed mode.02Assumptions and limits
Scope of validity
- Rigid body, fixed axis, I > 0; energy ≥ 0; inverse ω is a magnitude.
03Validation example
Reference numerical case
- I = 0.5 kg·m², ω = 10 rad/s: K = ½ × 0.5 × 10² = 25 J. Inverse modes return I = 0.5 kg·m² or |ω| = 10 rad/s.
04References
Technical references
FAQ
Why does moment of inertia matter for rotational energy?
Moment of inertia I measures how mass is distributed relative to the rotation axis. Rotational kinetic energy is K = ½Iω², so moving the same mass farther from the axis can increase I and the stored rotational energy at the same angular speed.
Can two objects with the same mass and angular speed have different rotational energy?
Yes. Equal mass does not imply equal moment of inertia. Different geometries or rotation axes can give different I values and therefore different rotational kinetic energies at the same ω.
05How it works
The moment of inertia describes how mass is distributed around an axis. At fixed I, doubling angular speed multiplies energy by four. A negative angular velocity gives the same energy as its positive counterpart; the inverse speed mode returns the nonnegative magnitude.
06Limits of the model
Classical rigid-body rotation about a fixed axis with constant positive I. Geometry, axis translation and internal energy are not modelled. Zero energy and zero angular speed cannot identify I; its inverse mode requires nonzero speed and positive energy.
07Common mistakes
Use mass moment of inertia in kg·m², not an area second moment in m⁴. Do not enter rpm as rad/s. Use the inertia about the specified axis; an inertia about another axis is not interchangeable.