Force and Motion

Before discussing AC motors it is necessary to understand some of the basic terminology associated with motor operation. Many of these terms are familiar to us in some other context. Later in the course we will see how these terms apply to AC motors.

Force In simple terms, a force is a push or a pull. Force may be caused by electromagnetism, gravity, or a combination of physical means. Net Force is the vector sum of all forces that act on an object, including friction and gravity. When forces are applied in the same direction, they are added. For example, if two 10 pound forces are applied in the same direction the net force would be 20 pounds

If 10 pounds of force is applied in one direction and 5 pounds of force is applied in the opposite direction, the net force would be 5 pounds and the object would move in the direction of the greater force.

If 10 pounds of force is applied equally in both directions, the net force would be zero and the object would not move.


Torque is a twisting or turning force that causes an object to rotate. For example, a force applied to the end of a lever causes a turning effect or torque at the pivot point. Torque (τ) is the product of force and radius (lever distance).

τ = Force x Radius

In the English system of measurements, torque is measured in pound-feet (lb-ft) or pound-inches (lb-in). For example, if 10 lbs of force is applied to a lever 1 foot long, the resulting torque is 10 lb-ft.

An increase in force or radius results in a corresponding increase in torque. Increasing the radius to two feet, for example, results in 20 lb-ft of torque.

An object in motion takes time to travel any distance. Speed is the ratio of the distance traveled and the time it takes to travel the distance.

Speed = Distance/Time

Linear speed is the rate at which an object travels a specified distance. Linear speed is expressed in units of distance divided by units of time, for example, miles per hour or meters per second (m/s). Therefore, if it take 2 seconds to travel 40 meters, the speed is 20 m/s.


The angular speed of a rotating object determines how long it takes for an object to rotate a specified angular distance. Angular speed is often expressed in revolutions per minute (RPM). For example, an object that makes ten complete revolutions in one minute, has a speed of 10 RPM.


An object can change speed. An increase in speed is called acceleration. Acceleration occurs only when there is a change in the force acting upon the object. An object can also change from a higher to a lower speed. This is known as deceleration (negative acceleration). A rotating object, for example, can accelerate from 10 RPM to 20 RPM, or decelerate from 20 RPM to 10 RPM


Mechanical systems are subject to the law of inertia. The law of inertia states that an object will tend to remain in its current state of rest or motion unless acted upon by an external force. This property of resistance to acceleration/deceleration is referred to as the moment of inertia. The English system unit of measurement for inertia is pound-feet squared (lb-ft2). For example, consider a machine that unwinds a large roll of paper. If the roll is not moving, it takes a force to overcome inertia and start the roll in motion. Once moving, it takes a force in the reverse direction to bring the roll to a stop

Any system in motion has losses that drain energy from the system. The law of inertia is still valid, however, because the system will remain in motion at constant speed if energy is added to the system to compensate for the losses. Friction occurs when objects contact one another. As we all know, when we try to move one object across the surface of another object, friction increases the force we must apply. Friction is one of the most significant causes of energy loss in a machine.

Whenever a force causes motion, work is accomplished. Work can be calculated simply by multiplying the force that causes the motion times the distance the force is applied.

Work = Force x Distance

Since work is the product of force times the distance applied, work can be expressed in any compound unit of force times distance. For example, in physics, work is commonly expressed in joules. 1 joule is equal to 1 newton-meter, a force of 1 newton for a distance of 1 meter. In the English system of measurements, work is often expressed in foot-pounds (ft-lb), where 1 ft-lb equals 1 foot times 1 pound.

Another often used quantity is power. Power is the rate of doing work or the amount of work done in a period of time. Power can be expressed in foot-pounds per second, but is often expressed in horsepower. This unit was defined in the 18 th century by James Watt. Watt sold steam engines and was asked how many horses one steam engine would replace. He had horses walk around a wheel that would lift a weight. He found that a horse would average about 550 foot-pounds ofwork per second. Therefore, one horsepower is equal to 550 foot-pounds per second or 33,000 foot-pounds per minute.


When applying the concept of horsepower to motors, it is useful to determine the amount of horsepower for a given amount of torque and speed. When torque is expressed in lb-ft and speed is expressed in RPM, the following formula can be used to calculate horsepower (HP). Note that an increase in torque, speed, or both increases horsepower.

power in HP = Torque in lb-ft x Speed in RPM/5252

Horsepower and Kilowatts AC motors manufactured in the United States are generally rated in horsepower, but motors manufactured in many other countries are generally rated in kilowatts (kW). Fortunately it is easy to convert between these units.

power in kW = 0.746 x power in HP

For example, a a motor rated for 25 HP motor is equivalent to a motor rated for 18
.65 kW.

0.746 x 25 HP = 18 .65 kW

Kilowatts can be converted to horsepower with the following formula.

power in HP = 1.34 x power in kW