PlanetPhysics/Power

Power

Power is the rate of [[../CosmologicalConstant/|energy]] transfer. Since there are several forms of energy, there are several ways of describing power. In general terms of energy, power is defined as

$P=\frac{dE}{dt}.$

Mechanical Power

The energy transfer in mechanical [[../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|systems]] where [[../Work/|work]] is done by an applied force

$P=\frac{dE}{dt}=\frac{dW}{dt}.$

Using the [[../Bijective/|relation]] between work and force

$dW=𝐅\cdot d𝐫$

and then differentiating to get power,

$P=\frac{dW}{dt}=𝐅\cdot \frac{d𝐫}{dt}=𝐅\cdot 𝐯.$

The corresponding form of power in rotation is

$P=𝐌\cdot \mathit{\omega },$

where $𝐌$ is the torque and $\mathit{\omega }$ the angular [[../Velocity/|velocity]] [[../Vectors/|vector]].

Electrical Power

Since energy is transfering from a device storing electrical energy to another device in the circuit that converts to another form of energy, power is the rate of change of electrical potential energy. For a DC circuit

$P=\frac{dU}{dt}=iV.$

Units

The SI unit of the power is one joule per second, which is called watt :

$\frac{\mathrm{J}}{\mathrm{s}}:=\mathrm{W}.$

The watt is equal to $\mathrm{k}\mathrm{g}\mathrm{\cdot }{\mathrm{m}}^{\mathrm{2}}/{\mathrm{s}}^{\mathrm{3}}$ in the base units.

The english units of power are

$1\left[horsepower\right]=1\left[hp\right]=550\left[\frac{ftlb}{s}\right]$

1 joule/second	= 1 watt
1,000 watts	= 1 kilowatt
746 watts	= 1 horsepower
550 ft-lb/sec	= 1 horsepower
33,000 ft-lb/min	= 1 horsepower