# 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 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

*P - power (W)*

* n _{m} - rotations (rpm)*

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})