A flywheel is a mechanical device with a significant moment of inertia used as a storage device for rotational energy. Flywheels resist changes in their rotational speed, which helps steady the rotation of the shaft when a fluctuating torque is exerted on it by its power source such as a pistonbased (reciprocating) engine, or when an intermittent load, such as a piston pump, is placed on it. Flywheels can be used to produce very high power pulses for experiments, where drawing the power from the public network would produce unacceptable spikes. A small motor can accelerate the flywheel between the pulses. Recently, flywheels have become the subject of extensive research as power storage devices for uses in vehicles and power plants; see flywheel energy storage.
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Energy is stored in the rotor as kinetic energy, or more specifically, rotational energy:
where
where m denotes mass, and r denotes a radius. More information can be found at list of moments of inertia
When calculating with SI units, the standards would be for mass, kilograms; for radius, meters; and for angular velocity, radians per second. The resulting answer would be in joules.
The amount of energy that can safely be stored in the rotor depends on the point at which the rotor will warp or shatter. The hoop stress on the rotor is a major consideration in the design of a flywheel energy storage system.
where
You can use those equations to do 'back of the envelope' calculations and find the rotational energy stored in various flywheels. I = kmr^{2}, and k is from List of moments of inertia
object  k (varies with shape)  mass  diameter  angular velocity  energy stored, J  energy stored 

bicycle wheel @ 20 km/h  1  1 kg  700 mm  150 rpm  15 J  4 × 10^{−3} Wh 
bicycle wheel, double speed (40 km/h)  1  1 kg  700 mm  300 rpm  60 J  16 × 10^{−3} Wh 
bicycle wheel, double mass (20 km/h)  1  2 kg  700 mm  150 rpm  30 J  8 × 10^{−3} Wh 
Flintstones concrete car wheel (19 km/h)  1/2  245 kg  500 mm  200 rpm  1.68 kJ  0.47 Wh 
wheel on train @ 60 km/h  1/2  942 kg  1 m  318 rpm  65 kJ  18 Wh 
giant dump truck wheel @ 30 km/h (18 mph)  1/2  1000 kg  2 m  79 rpm  17 kJ  4.8 Wh 
small flywheel battery  1/2  100 kg  600 mm  20000 rpm  9.8 MJ  2.7 kWh 
regenerative braking flywheel for trains  1/2  3000 kg  500 mm  8000 rpm  33 MJ  9.1 kWh 
electrical power backup flywheel  1/2  600 kg  500 mm  30000 rpm  92 MJ  26 kWh 
the planet Earth  2/5  5.97 × 10^{27} g  12,725 km  ~1 per day (696 µrpm^{[nb 1]})  2.6 × 10^{29} J  72 YWh (× 10^{24} Wh) 
See [6], [7], [8], [9], and Rotational energy
For a given flywheel design, it can be derived from the above equations that the kinetic energy is proportional to the ratio of the hoop stress to the material density.
This parameter could be called the specific tensile strength. The flywheel material with the highest specific tensile strength will yield the highest energy storage. This is one reason why carbon fiber is a material of interest.
In application of flywheels in vehicles, the phenomenon of precession has to be considered. A rotating flywheel responds to any momentum that tends to change the direction of its axis of rotation by a resulting precession rotation. A vehicle with a verticalaxis flywheel would experience a lateral momentum when passing the top of a hill or the bottom of a valley (roll momentum in response to a pitch change). Two counterrotating flywheels may be needed to eliminate this effect.
In a modern application, a momentum wheel is a type of flywheel useful in satellite pointing operations, in which the flywheels are used to point the satellite's instruments in the correct directions without the use of thruster rockets.
Flywheels are used in punching machines and riveting machines, where they store energy from the motor and release it during the operation cycle (punching and riveting).
The principle of the flywheel is found in the Neolithic spindle and the potter's wheel.^{[1]}
The Andalusian agronomist Ibn Bassal (fl. 10381075), in his Kitab alFilaha, describes the flywheel effect employed in a water wheel machine, the saqiya.^{[2]}
The flywheel as a general mechanical device for equalizing the speed of rotation is, according to the American medievalist Lynn White, recorded in the De diversibus artibus (On various arts) of the German artisan Theophilus Presbyter (ca. 10701125) who records applying the device in several of his machines.^{[1]}^{[3]}
In the Industrial Revolution, James Watt contributed to the development of the flywheel in the steam engine, and his contemporary James Pickard used a flywheel combined with a crank to transform reciprocating into rotary motion.
For internal combustion engine applications, the flywheel is a heavy wheel mounted on the crankshaft. Its main function is to maintain a fairly constant angular velocity of the crankshaft.
[[File:thumb180pxSimple flywheel in motion. Constructed based on drawings by Leonardo da Vinci]]
A flywheel is a heavy disk or wheel that is attached to a rotating shaft. Flywheels are used for storage of kinetic energy. The momentum of the flywheel causes it to not change its rotational speed easily. Because of this, flywheels help to keep the shaft rotating at the same speed. This helps when the torque applied to the shaft changes often. Uneven torque can change the speed of rotation. Because the flywheel resists changes in speed, it decreases the effects of uneven torque. Engines which use pistons to provide power usually have uneven torque and use flywheels to fix this problem.
It takes energy to get a wheel (any wheel) to rotate. If there is little friction (good bearings) then it will keep rotating a long time. When energy is needed, it can be taken from the wheel again. So it is a simple mechanical means of storing energy. The amount of energy stored is a function of the weight and the speed of rotation  making a heavier wheel rotate faster takes more energy. Another factor is the radius (size) because the farther from the axis a part of the wheel is, the more energy it takes to make is rotate. These three factor can be represented by M (mass), $\backslash omega$ (angular velocity) and R (radius). Combining the two equations below gives $\backslash omega$^{2}MR^{2}/4. A flywheel is not just any wheel, but specifically designed to store energy. So it should be heavy and/or rotate fast. For example, some buses have a flywheel that is used for stopping and starting. When the bus stops (eg for a traffic light), the flywheel is connected to the wheels, so the rotational energy is transferred to it, so the bus will slow down while the flywheel speeds up. Then, when the bus has to start driving again, it is connected again and the energy is transferred back. Of course, you wouldn't want to lug a heavy wheel around on a bus, so it is made of a lighter material that can withstand extremely fast rotation.
The kinetic energy of a rotating flywheel is
Where the moment of inertia of center mass is equal to
where $I$ is the moment of inertia of the mass about the center of rotation and $\backslash omega$ (omega) is the angular velocity in radian units.
The flywheel has been used since ancient times, the most common traditional example being the potter's wheel. In the Industrial Revolution, James Watt contributed to the development of the flywheel in the steam engine, and his contemporary James Pickard used a flywheel.
In the world of venture capital, the term "flywheel" is used to represent the recurrent, margingenerating heart of a business.
