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Mechanics
Mechanics

Rolling Kinetic Energy

KE=12mv2+12Iω2KE = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2

Total kinetic energy of a rolling object is the sum of translational and rotational kinetic energies.

Variables

KE
Total kinetic energy
Combined translational and rotational KE
J
m
Mass
Mass of rolling object
kg
v
Velocity
Center of mass velocity
m/s
I
Moment of inertia
About center of mass
kg·m²
ω
Angular velocity
Rate of rotation
rad/s

Derivation

KE_total = KE_trans + KE_rot = ½mv² + ½Iω². For rolling without slipping, v = ωR.

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Common questions

What is the Rolling Kinetic Energy formula?

Rolling Kinetic Energy is written KE = 1/2mv² + 1/2Iω². 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 = 1/2mv² + 1/2Iω²?

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 = 1/2mv² + 1/2Iω².