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# 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 nrps

= T π nrpm / 30                 (1)

where

P = power (W)

T = torque or moment (Nm)

π = 3.14...

nrps = rotations per second (rps, 1/s)

nrpm = rotations per minute (rpm, 1/min)

• rad = 360o / 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 nrpm / 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 nrpm

= 30 (2000 W) / (π (3600 rpm))

= 5.3 Nm

### Torque of a Body in Angular Motion

T = I α                    (2)

where

I = moment of inertia (kg m2, lbf ft s2)

## 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.

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.

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## Citation

• The Engineering ToolBox (2008). Angular Motion - Power and Torque. [online] Available at: https://www.engineeringtoolbox.com/angular-velocity-acceleration-power-torque-d_1397.html [Accessed Day Month Year].

Modify the access date according your visit.

9.27.11