# 2.2.2: Kinetic Energy

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Kinetic energy is the energy of a moving object, executing a linear motion or a rotational motion. For a solid object of mass m moving with a speed2 of v the formula for kinetic energy is:

$K = \frac 12 mv^2$

Moving fluids or gasses also carry kinetic energy, but the appropriate math formulae are more complicated – actually, about the kinetic energy carried by a moving gas (air) we will talk in the section “Wind Power”.

Kinetic energy in linear motion can hardly be used as a practical means of storing energy, because if one tried, the “reservoir would run away” :-). However, this is not the case with kinetic energy of rotational motion, i.e., of spinning object.

The kinetic energy of a spinning rigid solid body is given by:

$K = \frac 12 I \omega^2\;\;\;{\rm with}\;\;\; \omega = 2\pi f$

where $$f$$ is the number of revolutions per second executed by the spinning body, and I is a quantity called the moment of inertia, which depends on the mass, on the shape, and on the dimensions of the body in question. The formulae for moments of inertia of bodies of many different shapes can be readily found in the Web, for instance, in this Hyperphysics Web site.

In contrast to bodies moving along straight trajectories which are rather useless from the viewpoint of energy storing, spinning bodies can be used and are widely used for such storing. Such bodies are commonly known as “flywheels”. If a flywheel spins to fast, it may be torn apart by centrifugal forces – therefore, the the amount of energy that can be stored by a flywheel is not spectacular. One interesting idea that emerged in the middle of the last century was to use flywheels in public transportation, for propelling buses. After the flywheel in a such vehicle, called a “gyrobuses”, was “charged with energy” by en electric motor, it could run up to 6 km (about 3.5 miles). An advantage of gyrobuses was that they were very

“clean”, they emitted no fumes, in contrast to buses propelled by Diesel engines. However, there were many problems with maintaining fleets of such vehicles, so the initial enthusiasm gradually died out, and the several existing Gyrobus service systems in Europe and Africa were shut down by the end of the 1950-s.

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2Note that as a symbol of speed we use the same letter as we have used a moment ago for potential energy – but now we use a small letter for distinction. By the way, in “professional slang” big (capital) letters and small letters are often referred to as, respectively, “upper case letters” and “lower case letters”. Why? For historical reasons! You may find an explanation, e.g., in this Web document.

2.2.2: Kinetic Energy is shared under a CC BY 1.3 license and was authored, remixed, and/or curated by Tom Giebultowicz.