Force
Historically, the first mathematical description of interactions in Newtonian Mechanics. Forces produce a change in the motion of a mass on which they act, according to F=ma (Newton's Second Law), which is a vector equation (the acceleration is in the direction of the net force). Forces result from several types of physical interactions, which always exert opposite forces on two different objects (Newton's Third Law).
Motivation for Concept
Consider a bowling ball (or some other heavy object that moves with little resistance). If you want the ball to move, you have to exert a force on it in the direction you want it to move. If you want the moving ball to turn, you have to exert a force on it toward the side you want it to turn toward. If you want the ball to stop moving, you have to exert a force opposite to its velocity. To change the motion of the bowling ball, you will probably apply a force by using your hands or feet or some object you push against the ball. There are other kinds of forces, however. The earth, for example, can alter the ball's motion through the invisible action-at-a-distance of [gravity], often represented as a gravitational field acting on the body at the site of the body.
Newton's Laws
Newton's famous Three Laws of Motion together comprise his definition of force.
Newton's First Law
If an object is moving with no force acting upon it, then it will move with constant velocity. Note that velocity is a vector, so this statement implies that the object will keep the same speed and the same direction of motion. This directly contradicts the animistic view of motion in which the natural condition of a body is at rest with respect to its surroundings - the First Law says the natural state of a body is moving with zero acceleration, not zero velocity.
Newton's Second Law
The mathematical relationship between force and momentum, or, for systems with constant mass, the relationship between force and acceleration.
Newton's Third Law
Every force exerted on one body by a second body is paired with another force of equal magnitude and opposite direction exerted on the second body by the first.
">Newton's Third Law: Newton's Third Law
Every force exerted on one body by a second body is paired with another force of equal magnitude and opposite direction exerted on the second body by the first.
Classification of Forces
There are many ways to classify forces. For the purposes of the modeling approach to physics, the most important classifications to understand are Internal vs. External and Conservative vs. Non-Conservative. Another commonly encountered classification of forces is by their status as "fundamental" vs. phenomenological.