Forces and Motion


Glossary Definition for 16-19 IOP Glossary Project


Forces arise from interactions between objects, or between an object and a field. There are just four distinct ways in which particles can interact, giving rise to four distinct types of force. The four fundamental interactions and forces are:

  • gravitational (which acts between all matter)
  • electromagnetic (includes electrostatic and magnetic forces)
  • strong (very short range, acts between subatomic particles)
  • weak (very short range, acts between subatomic particles)

Generally, two objects can interact with more than one of these forces. Only the gravitational and electromagnetic forces are readily perceived in normal life although the strong and weak forces are important for the stability of nuclei.

Force is a vector quantity. Both the magnitude and direction of a force are important when determining its effects. A force is often represented by the symbol F.

When two objects interact, each exerts a force on the other; the forces are equal in size but opposite in direction.

Forces can do work by changing an object’s motion and/or deforming the object. For example, a single force acting on an object, F, changes the magnitude and/or direction of its momentum, p. This change in momentum is in the direction of the force. Force can be defined as rate of change of momentum:

F = dpdt

In situations where mass does not change, this is equivalent to the equation

F = ma

where a is the acceleration produced by the force and m is the mass of the object.


Forces may be attractive or repulsive. The force of gravity is always attractive. The electromagnetic force can be either attractive or repulsive: the force between two electric charges is attractive if the charges have opposite signs but repulsive if they have the same sign. The strong force is considered to be either always attractive, or to be attractive or repulsive, depending on which fundamental theory is used to describe it and on the separation between the particles concerned. The weak force may be attractive or repulsive, or neither, depending on certain properties of the particles concerned.

Our understanding of forces and their effects is summarised in Newton’s three laws of motion. They are classical laws, which means that they apply to situations where speeds are significantly less than the speed of light.

Newton’s first law of motion states that an object continues to move at constant velocity, or remains at rest, unless acted on by an unbalanced or resultant force.

Newton’s second law of motion relates an object’s rate of change of momentum to the resultant force acting on it.

Newton’s third law of motion states that all forces are the result of interactions. When two objects interact, each exerts a force on the other. The forces are equal in magnitude and opposite in direction, and act along the same line; they are both the same type of force (e.g. both gravitational).

Contact forces and friction are actually electromagnetic in origin. When a hand pushes on a door, there is an electromagnetic interaction between the electrons in the molecules at the surfaces of the hand and the door. However, in determining the motion of interacting objects, the nature of the forces(s) exerted on them is irrelevant; the only things that matter are the magnitude and direction of any forces and their lines of action.

SI unit

netwon, N

Expressed in SI base units

kg m s-2

Mathematical expressions

  • F = dpdt

    where p is the momentum of an object acted upon by a resultant force F.
  • F = ma

    where a is the acceleration of an object of mass m that is acted upon by a resultant force F.

Related entries

  • Potential energy
  • Work

In context

The expanding gases in a Rolls-Royce Griffon engine exert a force of magnitude up to around 11,000 N upon each piston head.

Two protons separated by 0.1 nm (1 × 10-10 m, a typical interatomic distance) repel each other with an electrostatic force of magnitude 2.3 × 10-8 N and attract one another with a gravitational force of magnitude 1.9 × 10-44 N.

The Earth and Sun attract each other with a gravitational force of magnitude 3.6 × 1022 N.


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