# Power

When you know the amount of energy that was required to move a particle you can then calculate the power that was used. Power is an integral of energy in respect to time. Refer to equation 1.

(Eq 1)  $P=F·V=\frac{dU}{dt}$

F = force

V = Velocity

P = Power

dU = Change in Energy

dt = Change in Time

Equation 1 represents the power input for a particle that has a linear projection. To calculate the power of a particle that has a rotational projection equation 2 would be used.

(Eq 2) $P=Tϖ$

T = Torque

ϖ = angular velocity

The units that represent power can be seen in equation 3.

(Eq 3)  $1W=1\frac{J}{S}=1\frac{N·m}{s},~or~1hp = 550\frac{ft·lb}{s}$

Finally, due to energy losses from friction or drag, the power that is put in will be more then the output power. To calculate the efficiency equation 4 would be used.

(Eq 4) $ε=\frac{energy~output}{energy~input}$