Rotational Kinetic Energy⚠ unverified
Physics / Mechanics · Compute rotational kinetic energy
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| moment_of_inertia | momentofinertia | kg*m^2 | 1.0 | Mass moment of inertia about the axis of rotation |
| angular_velocity | angularvelocity | rad/s | 1.0 | Angular velocity |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | KErot | J | Rotational kinetic energy, in joules (J) |
The science & history
Understanding the Parameters
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$I$ — depends on mass distribution and axis (Moment Of Inertia Disk, Moment Of Inertia Point Mass, Parallel Axis Theorem).
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$\omega$ — energy scales as $\omega^{2}$. Use rad/s (not rpm) unless converted: $\omega = 2\pi n/60$ for $n$ in rpm.
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$KE$ — energy stored in rotation; total KE of a rolling body is $\tfrac12 m v_{\mathrm{cm}}^{2} + \tfrac12 I_{\mathrm{cm}}\omega^{2}$.
Derivation (Approaching a Proof)
Each mass element has speed $v_i = r_i\omega$, so $KE = \sum \tfrac12 m_i v_i^{2} = \tfrac12\Bigl(\sum m_i r_i^{2}\Bigr)\omega^{2} = \tfrac12 I\omega^{2}$.
History
Rigid-body kinetic energy decomposition is classical (Euler); it is essential for flywheels, rotors, and rolling-without-slipping problems.
Related Concepts: Kinetic Energy, Moment Of Inertia Disk, Moment Of Inertia Point Mass, Torque, Power From Force Velocity
Notes: Registry calculator rotational-kinetic-energy (unverified). Single fixed axis; $\omega$
in rad/s.