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

Where,

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.