A force is an interaction between objects - a push or pull. This interaction has the ability to make an object speed up, slow down, change direction or change its shape.[1] Force is conventionally measured in units of newtons (N) or pounds (lbs).

Exerting a force over some distance represents a specific transfer of energy also known as work:

[math]W=\vec{F}\cdot\vec{d}=Fd \cos{\theta}[/math]

Where [math]W[/math] is work, [math]\vec{F}[/math] is the force, [math]\vec{d}[/math] is the amount of distance the force acts over and [math]\theta[/math] is the angle between the two.[2]

Fields (electric fields, magnetic fields, gravitational fields) are spatial regions that exert forces on objects.[3] The position of objects within these fields determines an object's potential energy. When an object is pushed opposite to a field (rocket flying upwards, against gravity), the object gains potential energy. An object that moves with a field loses potential energy and gains kinetic energy (or thermal energy). When forces move between potential and kinetic energy, the system is conserving mechanical energy. For example, if you roll a ball down a hill, the ball starts with potential energy, and as it rolls downward, it exchanges its potential energy with kinetic energy. If thermal energy is increased then there is still energy conservation, but it is more complicated.

Broadly, forces are either fundamental forces or everyday forces. [4]

PhET Simulation on Forces

The University of Colorado has graciously allowed us to use the following PhET simulation. This simulation demonstrates how forces affect motion and acceleration.

For Further Reading

For further information please see the related pages below:


  1. R. Chabay and B. Sherwood, "The Momentum Principle," in Matter & Interactions, 3rd ed., Hoboken, NJ: Wiley, 2011, ch.2, sec.2, pp. 50
  2. If the force is changing over the distance than calculus is required and [math]W=\int{\vec{F}\cdot d\vec{x}}[/math]
  3. R. D. Knight, "The concept of a field" in Physics for Scientists and Engineers: A Strategic Approach, 2nd ed. San Francisco, U.S.A.: Pearson Addison-Wesley, 2008, pp. 806
  4. Hyperphysics, Fundamental Forces [Online], Available: