Work: The result of a force acting over some distance. Quantified in joules (J = Nm) or foot-pounds (ft·lbf).
Torque: A rotating force produced by a motor’s crankshaft. A vector quantity acting in a rotational direction, commonly quantified in newton-metres (Nm) or pound-feet (lbf·ft).
Power: The rate at which work is accomplished—work done per unit of time. Quantified in watts (W = J/s) or horsepower (hp).

Power-Torque Relationships

The mechanical power of a rotating body can be calculated from torque and angular velocity:

$P = T \cdot \omega = T \cdot 2\pi \cdot n_{rps} = \frac{T \cdot \pi \cdot n_{rpm}}{30}$

where:

$P$ = power (W)
$T$ = torque (Nm)
$\omega$ = angular velocity (rad/s)
$n_{rps}$ = rotational speed (revolutions per second, 1/s)
$n_{rpm}$ = rotational speed (revolutions per minute, rpm)
$1 \text{ rad} = 360^\circ / 2\pi \approx 57.29578^\circ$

Note: An object (like an electric motor) can have an active torque without rotation, but without rotation ( $\omega = 0$ ), no power is produced.

Imperial Unit Form

$P = \frac{T \cdot n_{rpm}}{5252}$

where:

$P$ = power (hp)
$T$ = torque (lbf·ft)

Example: Torque from a Rotating Motor

An electric motor runs at 3600 rpm with a measured power consumption of 2000 W. The torque created by the motor (without losses) can be calculated by rearranging the power equation:

$T = \frac{30 P}{\pi \cdot n_{rpm}} = \frac{30 \cdot 2000}{\pi \cdot 3600} \approx 5.3 \text{ Nm}$

Torque and Angular Acceleration

The torque required to angularly accelerate a body is related to its moment of inertia and angular acceleration:

$T = I \cdot \alpha$

where:

$I$ = moment of inertia (kg·m² or lbf·ft·s²)
$\alpha$ = angular acceleration (rad/s²)

Source: engineeringtoolbox.com