Kinetic energy is the energy associated with motion. In classical mechanics, translational kinetic energy grows with mass and with the square of speed, which is why speed changes have a disproportionately large effect on energy.
Definition (translation)
For a body of mass m moving with speed v:
K = 1/2 m v^2
The SI unit is the joule (J).
Work–energy theorem
Net work done on a body equals the change in its kinetic energy:
W_net = ∫ F · dr = ΔK
This connects forces (dynamics) to energy changes without explicitly solving for motion as a function of time.
Relation to momentum
For constant mass, p = m v, so kinetic energy can be written as
K = p^2 / (2m)
This is useful when momentum is the natural conserved quantity (collisions) but you want an energy estimate.
Rotational kinetic energy
For rotation with angular speed ω and moment of inertia I:
K_rot = 1/2 I ω^2
For rigid-body motion, total kinetic energy splits into translation of the center of mass plus rotation about it.
Collisions and energy
In an isolated system, momentum is conserved. Kinetic energy is conserved only for elastic collisions. In inelastic collisions, some kinetic energy is converted to internal energy (heat), sound, permanent deformation, etc.
Common pitfalls
- K depends on speed (a scalar), not velocity direction, and is always ≥ 0.
- Doubling speed quadruples kinetic energy.