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 foot-pounds.
- 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 pound-feet.
- 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 lbf )
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 m2, lbf ft s2)
α = angular acceleration ( rad /s2)
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