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Physics: Problems and Solutions

Power

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Power is the rate at which work is done, or the derivative of work with respect to time. The SI unit is the watt (W, equal to J/s). The formula for power is

P_\mathrm{avg} = \frac{\Delta W}{\Delta t}\,
P = \lim _{\Delta t\rightarrow 0} \frac{\Delta W}{\Delta t} =  \frac{\mathrm{d}W}{\mathrm{d}t}\,

One can easily see that this is the same as the dot product of force and velocity. In rotational systems, power is equal to the dot product of torque (τ) and angular velocity (ω, measured in radians per second),

P(t) = \tau \cdot \omega

As the derivative of work, power comes in many forms. In the case of an electric circuit, power is equal to

P = IV = I^2 R = \frac{V^2}{R}

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