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Torque and power

The mechanical power from a motor is torque times angular velocity. The same power can come as high torque at low speed or low torque at high speed. That is why gears are used to match the motor to the load.

P = M\,\omega

mechanical power

\omega = \frac{2\pi n}{60}

angular velocity from speed

Symbols

$P$	power	W
$M$	torque	Nm
$\omega$	angular velocity	rad/s
$n$	speed	rpm

Example

A motor at 1440 rpm giving 50 Nm:

$\omega \approx 150.8$ rad/s and $P \approx 7.5$ kW.

Remember to convert from rpm to rad/s before multiplying by the torque.

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Part of Electric Power and Machines: Electric motors.