quality:correction
Mechanical advantage

If a mechanical system has no losses, then the input power must equal the output power. This provides a simple formula for the mechanical advantage of the system.

Let the input power to a device be a force F acting on a point that moves with velocity v and the output power be a force F acts on a point that moves with velocity v. If there are no losses in the system, then P = F B v B = F A v A, {\displaystyle P=F_{\text{B}}v_{\text{B}}=F_{\text{A}}v_{\text{A}},} and the mechanical advantage of the system (output force per input force) is given by M A = F B F A = v A v B. {\displaystyle \mathrm {MA} ={\frac {F_{\text{B}}}{F_{\text{A}}}}={\frac {v_{\text{A}}}{v_{\text{B}}}}.}

The similar relationship is obtained for rotating systems, where T and ω are the torque and angular velocity of the input and T and ω are the torque and angular velocity of the output. If there are no losses in the system, then P = T A ω A = T B ω B, {\displaystyle P=T_{\text{A}}\omega _{\text{A}}=T_{\text{B}}\omega _{\text{B}},} which yields the mechanical advantage M A = T B T A = ω A ω B. {\displaystyle \mathrm {MA} ={\frac {T_{\text{B}}}{T_{\text{A}}}}={\frac {\omega _{\text{A}}}{\omega _{\text{B}}}}.}

These relations are important because they define the maximum performance of a device in terms of velocity ratios determined by its physical dimensions. See for example gear ratios.