Kinetic energy is the energy associated with the motion of a body. Whenever a body moves it possesses a reserve of energy proportional to its mass and to the square of its speed: it is this energy that a moving body can hand over to the other bodies it interacts with, for example by deforming them, heating them, or setting them in motion in turn.

In the language of energy-exchange diagrams, kinetic energy is one of the fundamental “bubbles”: a reservoir that fills and empties as forces do work on the body.

Energy-exchange diagram. Each “bubble” holds one type of energy with its initial value (top) and final value (bottom). Arrows indicate transfers. Only arrows crossing the system boundary change the total energy.

Principle — Kinetic energy

Ecin=12mv2\ev{E_{\text{cin}} = \frac{1}{2}\,m\,|\vec{v}|^2}

Key formula

Ecin=12mv2E_{\text{cin}} = \frac{1}{2}mv^2 It depends on the magnitude of v\vec{v}, not on its direction!

Two properties make kinetic energy particularly easy to handle. The first is that it is always positive or zero: the square of the speed can never be negative, and it vanishes only when the body is at rest. The second is that it does not depend on the direction of motion, only on how fast the body is moving. A car travelling at 100  km/h100\;\text{km/h} northwards has exactly the same kinetic energy as one travelling at 100  km/h100\;\text{km/h} eastwards: changing direction, at the same speed, does not change the kinetic energy. It is precisely this insensitivity to direction that distinguishes energy — a scalar quantity — from momentum, which is instead a vector.

Topics: Lavoro ed energia Concepts: Energia cinetica Skills: Bilancio energetico a bolle Methods: Diagramma a bolle di scambio energetico

Related exercises: Problem — Kinetic energy of a ball · Problem — True or false on work and energy · Problem — Estimating the kinetic energy of a car