Time Power: A Proven System for Getting More Done in Less Time Than You Ever Thought Possible

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If a constant force F is applied throughout a distance x, the work done is defined as W = F ⋅ x {\displaystyle W=\mathbf {F} \cdot \mathbf {x} } .

The similar relationship is obtained for rotating systems, where T A and ω A are the torque and angular velocity of the input and T B and ω B are the torque and angular velocity of the output. Likewise, the power dissipated in an electrical element of a circuit is the product of the current flowing through the element and of the voltage across the element. Other units of power include ergs per second (erg/s), foot-pounds per minute, dBm, a logarithmic measure relative to a reference of 1 milliwatt, calories per hour, BTU per hour (BTU/h), and tons of refrigeration. Mechanical power [ edit ] One metric horsepower is needed to lift 75 kilograms by 1 metre in 1 second.Instantaneous power is the limiting value of the average power as the time interval Δ t approaches zero. displaystyle \mathrm {MA} ={\frac {T_{\text{B}}}{T_{\text{A}}}}={\frac {\omega _{\text{A}}}{\omega _{\text{B}}}}.

displaystyle P={\frac {dW}{dt}}={\frac {d}{dt}}\left(\mathbf {F} \cdot \mathbf {x} \right)=\mathbf {F} \cdot {\frac {d\mathbf {x} }{dt}}=\mathbf {F} \cdot \mathbf {v} . In particular, power is the product of a force on an object and the object's velocity, or the product of a torque on a shaft and the shaft's angular velocity.displaystyle P={\frac {dW}{dt}}={\frac {d}{dt}}\int _{\Delta t}\mathbf {F} \cdot \mathbf {v} \,dt=\mathbf {F} \cdot \mathbf {v} . These relations are important because they define the maximum performance of a device in terms of velocity ratios determined by its physical dimensions. As a simple example, burning one kilogram of coal releases more energy than detonating a kilogram of TNT, [6] but because the TNT reaction releases energy more quickly, it delivers more power than the coal.