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

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The ratio of the pulse duration to the period is equal to the ratio of the average power to the peak power. displaystyle P=\lim _{\Delta t\to 0}P_{\mathrm {avg} }=\lim _{\Delta t\to 0}{\frac {\Delta W}{\Delta t}}={\frac {dW}{dt}}. These relations are important because they define the maximum performance of a device in terms of velocity ratios determined by its physical dimensions. 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.

Instantaneous power is the limiting value of the average power as the time interval Δ t approaches zero. 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} . displaystyle \mathrm {MA} ={\frac {T_{\text{B}}}{T_{\text{A}}}}={\frac {\omega _{\text{A}}}{\omega _{\text{B}}}}.displaystyle W=\int _{C}\mathbf {F} \cdot d\mathbf {r} =\int _{\Delta t}\mathbf {F} \cdot {\frac {d\mathbf {r} }{dt}}\ dt=\int _{\Delta t}\mathbf {F} \cdot \mathbf {v} \,dt. In the International System of Units (SI), the unit of power is the watt (W), which is equal to one joule per second.

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.P ( t ) = p Q , {\displaystyle P(t)=pQ,} where p is pressure in pascals or N/m 2, and Q is volumetric flow rate in m 3/s in SI units. Specifying power in particular systems may require attention to other quantities; for example, the power involved in moving a ground vehicle is the product of the aerodynamic drag plus traction force on the wheels, and the velocity of the vehicle. 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. Peak power and duty cycle [ edit ] In a train of identical pulses, the instantaneous power is a periodic function of time. In the case of a periodic signal s ( t ) {\displaystyle s(t)} of period T {\displaystyle T} , like a train of identical pulses, the instantaneous power p ( t ) = | s ( t ) | 2 {\textstyle p(t)=|s(t)|

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. displaystyle \mathrm {MA} ={\frac {F_{\text{B}}}{F_{\text{A}}}}={\frac {v_{\text{A}}}{v_{\text{B}}}}. The output power of a motor is the product of the torque that the motor generates and the angular velocity of its output shaft. 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.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} } .