Torque  Work done and Power Transmitted
The work done and power transmitted by a constant torque.
Work done
Work done is the force multiplied with the distance moved by the force  and can be expressed as
W = F s (1)
where
W = work done (J, Nm)
F = force (N)
s = distance moved by force (s)
For an angular motion
the work done can be expressed as
W = F θ r
= T θ (2)
where
W = work (Joules)
θ = angle (radians)
r = radius (m)
T = torque or moment (Nm)
Power transmitted
Power is the ratio between the work done and the time taken and can be expressed as
P = W / dt
= T θ / dt
= T ω
= 2 π n T
= 2 π (n_{rpm }/ 60) T
= 0.105 n_{rpm} T (3)
where
P = power (Watts)
dt = time taken (s)
ω = θ / dt = 2 π n = angular velocity (rad/s)
n = speed (rev/s)
n_{rpm} = speed (rev/min, rpm)
Note!  a machine must rotate to produce power! A machine with no rotation can deliver torque  like an electric motor  but since no distance is moved by force  no power is produced. As soon as the machine starts to rotate power is produced.
Example  required Torque to produce Power
A machine rotates with speed 3000 rev/min (rpm) and consumes 5 kW. The torque at the shaft can be calculated by modifying (3) to
T = P / 2 π n
= (5 kW) (1000 W/kW) / 2 π (3000 rev/min) / (60 sec/min)
= 15.9 Nm
Related Topics

Mechanics
The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
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