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.

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.

Internal vs. External

• Internal Force: A force exerted on one constituent of a specified system by another constituent of the same system. Internal forces do not affect the momentum of the system's center of mass, because their effects always cancel as required by Newton's Third Law.

• External Force: A force exerted on a constituent of a system by the environment.

Conservative vs. Non-Conservative

• Conservative Force: A force which has an associated potential energy. In introductory mechanics, the only conservative forces generally encountered are gravitation (universal) and elastic forces which satisfy Hooke's Law for elastic interactions.

• Non-Conservative Forces: A force which does work on an object in a path-dependent manner. For example, any force that has more than one possible value at a specific position is non-conservative.

Fundamental vs. Phenomenological

• Fundamental Forces: Forces which can influence the motion of at least one class of elementary fermionic particle. The only fundamental force which is studied directly in introductory mechanics is gravity.

• Phenomenological Forces: The page phenomenological force could not be found.