Angular velocity and acceleration - power and torque

Power and Moment of Body in Angular Motion

The power of a rotating body can be expressed as

P = T ω        

   = T 2 π n_rps   

   = T π n_rpm / 30                 (1)

where

P = power (W)

T = torque or moment (Nm)

ω = angular velocity (rad/s)

π = 3.14...

n_rps = rotations per second (rps, 1/s)

n_rpm = rotations per minute (rpm, 1/min)

• 1 rad = 360^o / 2 π =~ 57.29578..^o

Note! - an object - like an electric motor - can have an active moment without rotation, but without rotation (ω = 0) there is no power produced.    

In imperial units

P = T n_rpm / 5252                   (1b)

where

P = power (hp)

T = torque (lb_f ft)  

Example - Moment created by a Rotating Motor

An electric motor runs with 3600 rpm with an measured power consumption of 2000 W. The moment created by the motor (without losses) can be calculated by rearranging (1) to

T = 30 P / (π n_rpm) 

   = 30 (2000 W) / (π (3600 rpm))  

   = 5.3 Nm