In physics and other sciences, a **force** is a push or pull on a mass that can change the object’s motion. Force is a vector quantity, meaning it has both magnitude and direction. The symbol for force is the capitol letter F. A famous example of an equation for force is Newton’s second law:

**F = m*a**

Here F is force, m is mass, and a is acceleration. This law states that a net force equals the rate of the change of its momentum with time. Assuming mass is constant, the object’s acceleration (change in velocity) is directly proportional to the force and in the direction of the force.

### Units of Force

The SI unit of force is the newton (N), which is a kilogram meter per second squared (kg**·**m/s^{2}). Other common units include:

- dyne
- kilogram-force (kilopond)
- poundal
- kip
- pound-force

### History

The Greek philosophers Aristotle and Archimedes studied force, but believed constant motion requires a constantly applied force. Galileo Galilei and Sir Isaac Newton corrected this misperception and described force mathematically. Galileo’s inclined plane experiment (1638) mathematically described naturally accelerated motion. Newton’s three laws of motion (1687) describe force under ordinary conditions. Einstein’s theory of relativity expands the describes phenomena occurring close to the speed of light.

In a nutshell, Newton’s three laws of motions are:

- A body in motion stays in motion at a constant velocity unless acted upon by an external force. Similarly, a body at rest stays at rest unless acted upon by an external force.
- The force on an object equals the object’s mass multiplied by its acceleration.
- When one object exerts a force on another object, the second object exerts an equal and opposite force on the first.

### Examples of Forces

Forces exist all around us in the everyday world. For example:

- Friction is a force that opposes motion.
- Applied force is the force applied to an object by a person or other object.
- Centripetal force is a force acting on a body moving in a circular path that is directed toward the center of the circle.
- Centrifugal force is an apparent force that acts outward on a rotating body.
- The normal force is the force exerted upon an object that is in contact with a surface.
- The force of gravity is the attractive force between two masses. Weight is the acceleration due to gravity multiplied by an object’s mass.
- The tension force is the force that pulls equally on two objects connected by a string, wire, or robe.
- Spring force is the force exerted by a stretched or compressed spring.
- The Coriolis force acts perpendicular to the direction of motion and axis of rotation on a mass moving in a rotating system.
- The electromagnetic force is the attraction between opposite electrical charges or magnetic poles, or repulsion of like charges or magnetic poles.

### The Fundamental Forces

The four fundamental forces of nature are gravity, electromagnetism, the strong interaction, and the weak interaction.

- Gravity is the attractive force between two masses. It acts over an infinite distance, but is the weakest of the fundamental forces.
- Electromagnetism describes the attraction and repulsions of electrical charges and magnets. Like gravity, it is effective over an infinite distance.
- The weak interaction affects some nuclear phenomena, like beta decay. Its effective range is only about 10
^{-18}meters, so it acts on the atomic scale. - The strong interaction is very powerful, but it only acts over a range of about 10
^{-15}meters. Among other things, it binds protons and neutrons together within the atomic nucleus.

### References

- Corben, H.C.; Stehle, Philip (1994).
*Classical Mechanics*. New York: Dover Publications. ISBN 978-0-486-68063-7. - Cutnell, John D.; Johnson, Kenneth W. (2003).
*Physics*(6th ed.). Hoboken, New Jersey: John Wiley & Sons Inc. ISBN 978-0471151838. - Hellingman, C. (1992). “Newton’s third law revisited”. Phys. Educ. 27 (2): 112–115. doi:10.1088/0031-9120/27/2/011
- Newton, Isaac (1999).
*The Principia Mathematical Principles of Natural Philosophy*. Berkeley: University of California Press. ISBN 978-0-520-08817-7. - Sears, F.; Zemansky, M.; Young, H. (1982).
*University Physics*. Reading, Massachusetts: Addison-Wesley. ISBN 978-0-201-07199-3.