# 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

### • Dynamics

Motion - velocity and acceleration, forces and torque.

## Related Documents

### Conn-Rod Mechanism

The connecting rod mechanism.

### Conservation of Momentum

The momentum of a body is the product of its mass and velocity - recoil calculator.

### Distance Traveled vs. Speed and Time - Calculator and Chart

Velocity plotted in time used diagram.

### Electric Motors - IEC and NEMA Standard Torques

IEC and NEMA torque classifications of electrical motors.

### Electric Motors - Torque vs. Power and Speed

Electric motor output power and torque vs. rotation speed.

### Flywheels - Kinetic Energy

The kinetic energy stored in flywheels - the moment of inertia.

### Formulas of Motion - Linear and Circular

Linear and angular (rotation) acceleration, velocity, speed and distance.

### Improvised Torque Wrench

Improvise a torque wrench with a luggage scale.

### Impulse and Impulse Force

Forces acting a very short time are called impulse forces.

### Kinetic Energy

Energy possessed by an object's motion is kinetic energy.

### Power

Power is the rate at which work is done or energy converted.

### Projectile Range

Calculate the range of a projectile - a motion in two dimensions.

### Radians vs. Degrees

Radian is the SI unit of angle. Convert between degrees and radians. Calculate angular velocity.

### Velocity Units Converter

Convert between speed and velocity units like *m/s, km/h, knots, mph and ft/s*.