Think through a pulley of radius (R) and force (F) is applied as shown in the Fig.
then, torque T = F x R Nm
Let speed of pulley is N revolutions per minute. Now work done in one revolution is force into distance travelled in one revolution.
d = distance travelled in 1 revolution
d = 2πR
W = work done in 1 revolution
∴ W = F x d
= 2 π R F J
The time required for a revolution can be obtained from speed N r.p.m.
t = time for a revolution
t = (60/N) sec
Now Power (P) = W/t
P = (2 π R F) / (60/N)
Rewrite as P = [(2 π N)/60] X [FxR]
∴ P = T x ω
torque T = (F x R) in Nm
angular velocity ω =[(2 π N)/60] in rad/sec.
The relation P = T x ω is very important in evaluating numerous mechanical system.