Work done
Work done is 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 work done and time taken and can be expressed as
P = W / dt
= T θ / dt
= T ω
= 2 π n T (3)
where
P = power (Watts)
dt = time taken (s)
ω = θ / dt = 2 π n = angular velocity (rad/s)
n = speed (rev/s)
Example - Required Power
A machine rotating with speed 3000 rev/min (rpm) 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 sek/min)
= 15.9 Nm
