Mechanics
Rotational Kinetic Energy
Kinetic energy due to rotational motion.
Variables
KErotJ
Rotational KE
Energy of rotation
In SI units: kg·m²/s²
Allowed values: 0 or more
Ikg·m²
Moment of inertia
Rotational inertia
Allowed values: 0 or more
ωrad/s
Angular velocity
Rate of rotation
Derivation
Rotational analog of KE = ½mv².
Your notes
0/5000
Check value
Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- I = 2 kg·m² (Moment of inertia)
- ω = 3 rad/s (Angular velocity)
Result: KErot = 9 J
Other mechanics formulas with the same quantities
- Angular Momentum (Rotational Motion) shares Moment of inertia, Angular velocity
- Rolling Kinetic Energy (Rotational Motion) shares Moment of inertia, Angular velocity
- Angular Velocity (Rotational Motion) shares Angular velocity
- Linear-Angular Velocity Relation (Rotational Motion) shares Angular velocity
- Centripetal Acceleration (Rotational Motion) shares Angular velocity
- Newton's Second Law (Rotation) (Rotational Motion) shares Moment of inertia
Where this formula is listed
- Mechanics formulas, under Rotational Motion, alongside Angular Acceleration, Centripetal Force, Torque, Rotational Kinematic 1 and Rotational Kinematic 2.
- In the mechanics list it comes after Newton's Second Law (Rotation) and before Angular Momentum.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Rotational Kinetic Energy formula?
Rotational Kinetic Energy is written KE_rot = (1/2)Iω². Kinetic energy due to rotational motion. It belongs to Mechanics, under Rotational Motion.
What are the units in KE_rot = (1/2)Iω²?
In SI units, KE_r ot is rotational ke, measured in kg·m²/s²; I is moment of inertia, measured in kg·m²; ω is angular velocity, measured in rad/s.
How is the Rotational Kinetic Energy formula derived?
Rotational analog of KE = ½mv². The result is KE_rot = (1/2)Iω².