Angular Motion  Power and Torque
Angular velocity and acceleration vs. power and torque.
 Work is the result of a force acting over some distance. Work is quantified in joules (Nm) or footpounds.
 Torque is a rotating force produced by a motor’s crankshaft. The more torque the motor produces, the greater is its ability to perform work. Since torque is a vector acting in a direction it is commonly quantified by the units Nm or poundfeet.
 Power is how rapidly work is accomplished  work in a given amount of time. Power is quantified in watts (J/s) or horse power.
Power and Torque 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 (ft lb _{ f } )
Example  Torque created by Rotating Motor
An electric motor runs with 3600 rpm with an measured power consumption of 2000 W . The torque 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
Torque Calculator
Download and print Motor  Torque vs. Power and rpm chart
Torque of a Body in Angular Motion
T = I α (2)
where
I = moment of inertia (kg m^{2}, lb _{ f } ft s^{2})
α = angular acceleration ( rad /s^{2})
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