Kinetic energy

Kinetic energy is the energy something has because it is moving. In classical physics, for an object that is not spinning, with mass m and speed v, this energy equals ½mv². This amount is also the work—force multiplied by the distance over which it acts—needed to bring the object from rest to that speed, and the same work is released when the object slows back to rest. The standard unit is the joule; the older English unit is the foot-pound. In relativistic physics, the formula ½mv² is only accurate when the speed is much smaller than light’s speed.

The word “kinetic” comes from the Greek *kinesis*, meaning motion. The distinction between kinetic and potential energy goes back to Aristotle’s ideas of actuality and potentiality. The principle that kinetic energy is proportional to mass times velocity squared was worked out by Gottfried Leibniz and Johann Bernoulli, who called it *vis viva*, or “living force.” In 1722, Willem ’s Gravesande dropped weights into clay and found that the depth they sank was proportional to the square of their impact speed. Émilie du Châtelet saw the importance of this experiment and published the first explanation of the relation for kinetic energy. The modern terms “kinetic energy” and “work” date from the mid-1800s. Thomas Young, in a 1802 lecture, was the first to use “energy” in its current sense for motion energy, instead of *vis viva*. Gaspard-Gustave Coriolis published the mathematics of kinetic energy in 1829. William Thomson (later Lord Kelvin) coined the phrase “kinetic energy” around 1849–1851. William Rankine introduced “potential energy” in 1853 and used “actual energy” as its opposite, but later noted that Thomson and Peter Tait replaced “actual” with “kinetic.”

Energy appears in many forms—chemical, thermal, electromagnetic, gravitational, electric, elastic, nuclear, and rest energy—which fall into two main groups: potential and kinetic. Kinetic energy is the energy of movement. It can be passed between objects or changed into other energy types. A cyclist, for example, turns chemical energy from food into kinetic energy while speeding up. On flat ground, no extra work is needed to keep that speed except to fight air resistance and friction; the process is not perfectly efficient and produces some heat. If the cyclist coasts up a hill and stops at the top, most of the kinetic energy has become gravitational potential energy, which can be released going downhill. Friction steals some energy, so the cyclist never gets back to full speed without pedaling again—but the energy is not destroyed, just converted. If a dynamo is attached to a wheel, some kinetic energy becomes electrical energy, and the bike slows more. Braking turns kinetic energy into heat through friction.

Like any velocity-dependent quantity, kinetic energy depends on the observer’s frame of reference—it is not the same for all observers. Spacecraft burn chemical fuel to gain huge kinetic energy and reach orbital speed. In a perfect circular orbit, that kinetic energy stays nearly constant because space has almost no friction. At re-entry, some kinetic energy turns into heat. In an elliptical or hyperbolic orbit, kinetic and potential energy swap back and forth: kinetic energy is highest and potential lowest at the closest point to Earth, and the reverse at the farthest point. The total of kinetic plus potential energy remains constant, ignoring gains or losses. Kinetic energy can also be transferred between objects. In billiards, a player gives kinetic energy to the cue ball with a strike. When the cue ball hits another ball, it slows and the second ball speeds up, passing the energy along. Such collisions are nearly elastic, so kinetic energy is mostly preserved. In inelastic collisions, kinetic energy is lost to heat, sound, or binding energy.