Rolling Kinetic Energy
Total kinetic energy of a rolling object is the sum of translational and rotational kinetic energies.
Variables
Derivation
KE_total = KE_trans + KE_rot = ½mv² + ½Iω². For rolling without slipping, v = ωR.
Your notes
Check value
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- m = 2 kg (Mass)
- v = 3 m/s (Velocity)
- I = 4 kg·m² (Moment of inertia)
- ω = 5 rad/s (Angular velocity)
Result: KE = 59 J
Other mechanics formulas with the same quantities
- Moment of Inertia (Point Mass) (Rotational Motion) shares Moment of inertia, Mass
- Angular Momentum (Rotational Motion) shares Moment of inertia, Angular velocity
- Angular Velocity (Rotational Motion) shares Angular velocity
- Centripetal Acceleration (Rotational Motion) shares Angular velocity
- Centripetal Force (Rotational Motion) shares Mass
- Newton's Second Law (Rotation) (Rotational Motion) shares Moment of inertia
Where this formula is listed
- Mechanics formulas, under Rotational Motion, alongside Angular Acceleration, Torque, Rotational Kinematic 1, Rotational Kinematic 2 and Rotational Kinematic 3.
- In the mechanics list it comes after Parallel Axis Theorem and before Universal Gravitation.
- 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 Rolling Kinetic Energy formula?
Rolling Kinetic Energy is written KE = (1/2)mv² + (1/2)Iω². Total kinetic energy of a rolling object is the sum of translational and rotational kinetic energies. It belongs to Mechanics, under Rotational Motion.
What are the units in KE = (1/2)mv² + (1/2)Iω²?
In SI units, KE is total kinetic energy, measured in kg·m²/s²; m is mass, measured in kg; v is velocity, measured in m/s; I is moment of inertia, measured in kg·m²; ω is angular velocity, measured in rad/s.
How is the Rolling Kinetic Energy formula derived?
KE_total = KE_trans + KE_rot = ½mv² + ½Iω². For rolling without slipping, v = ωR. The result is KE = (1/2)mv² + (1/2)Iω².