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Angular Motion - Power and Torque

Angular velocity and acceleration - power and torque

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Power and Moment of Body in Angular Motion

The power of a rotating body can be expressed as

P = T ω        

   = T 2 π nrps  

   = T π nrpm / 30                 (1)

where

P = power (W)

T = torque or moment (Nm)

ω = angular velocity (rad/s)

π = 3.14...

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

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

  • rad = 360o / 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 nrpm / 5252                   (1b)

where

P = power (hp)

T = torque (lbf 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 nrpm

   = 30 (2000 W) / (π (3600 rpm))  

   = 5.3 Nm

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P - power (W)

nm - rotations (rpm)


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Torque of a Body in Angular Motion

T = I α                    (2)

where

I = moment of inertia (kg m2, lbm ft2)

α = angular acceleration (rad/s2)

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Length

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in
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Volume

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kgf
N
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Pressure

Pa (N/m2)
bar
mm H2O
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psi
inches H2O


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Flow

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US gpm
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