# Angular Motion - 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 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 = Iα (2)

where

I = moment of inertia (kg m^{2}, lb_{f}ft s^{2})

α = angular acceleration ( rad /s^{2})

## Related Topics

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