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# 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)

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 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)

## Related Topics

### • Dynamics

Motion of bodies and the action of forces in producing or changing their motion - velocity and acceleration, forces and torque.

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### Conservation of Momentum

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

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### 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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