Q:

Unknown $c$ in torque equations

In a book I have come across a couple of unrelated equations with an unknown $c$, in equations of the form
$$T_{en} = \frac{P_{en}}{2\pi n_n}c,$$
where $T_{en}$ is torque, $P_{en}$ is rated power and $n_{n}$ is speed in rpm. The book does not mention the $c$ at all and my first thought was it was a constant but is it possible it has a value and the book has made an error in not saying what it denotes?

A:

I $c$ bet it is a unit conversion number. The value would depends on the units used for torque, power, and speed. In the SI system $$ T = \frac{P}{\omega} $$ where $P$ is power in $[\mbox{W}]$, $T$ is torque in $[\mbox{N m}]$ and $\omega$ rotational speed in $[\mbox{rad/sec}]$.
If you convert rotational speed from radians per second to rpm you get $n = 60 \frac{\omega}{2\pi}$ or
$$ T = 60 \frac{P}{2\pi n} $$
Where $n$ is rotational speed in $[\mbox{rpm}]$.

