Reaction (physics)
Encyclopedia
The third of Newton's laws of motion
Newton's laws of motion
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...

of classical mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

states that force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

s always occur in pairs. Every action is accompanied by a reaction of equal magnitude but opposite direction. This principle is commonly known in the Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

language as actio et reactio. The attribution of which of the two forces is action or reaction is arbitrary. Each of the two forces can be considered the action, the other force is its associated reaction.

Discussion

The reaction is one of the least understood of the basic physical concepts, perhaps because it is often poorly taught or incorrectly described in many publications, including textbooks, or because Newton's laws of motion
Newton's laws of motion
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...

may appear counter-intuitive. A modern statement of the third law of motion is
If a force acts upon a body, then an equal and opposite force must act upon the body that exerts the force.

It is essential to understand that the reaction applies to another body (the body that exerts the force) than the one on which the action applies. For example, in the context of gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

, when object A attracts object B (action), then object B simultaneously attracts object A, with the same intensity and an opposite direction.

The physical nature of the reaction is identical to that of the action. If the action is due to gravity, the reaction is also due to gravity.

Examples of correct interpretations

• The Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

orbits around the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

because the gravitational force exerted by the Sun on the Earth, the action, serves as the centripetal force
Centripetal force
Centripetal force is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens...

that maintains the planet in the neighborhood of the Sun. Simultaneously, the Earth exerts a gravitational attraction on the Sun, the reaction, which has the same amplitude as the action and an opposite direction (in this case, pulling the Sun towards the Earth). Since the Sun's mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

is very much larger than the Earth's, it does not appear to be reacting to the pull of the Earth, but in fact it does. A correct way of describing the combined motion of both objects (ignoring all other celestial bodies for the moment) is to say that they both orbit around the center of mass
Center of mass
In physics, the center of mass or barycenter of a system is the average location of all of its mass. In the case of a rigid body, the position of the center of mass is fixed in relation to the body...

of the combined system.
• Consider a mass hanging at the end of a non-stretchable cable attached to the ceiling of a laboratory. The mass is pulled towards the Earth (action) by its weight
Weight
In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude , often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus:...

. The corresponding reaction is the gravitational force that mass exerts on the planet: this has nothing to do with the presence of the cable as the same reaction would also exist in the absence of the cable. On the other hand, if the tension in the cable is pulling the mass upwards and preventing it from falling, then the mass is simultaneously pulling on the cable, with equal intensity and opposite direction. If this simple system is observed to be at rest (in particular not accelerated) with respect to the ceiling, Newton's first law implies that no net force is applied to the mass. Since we have just seen that two distinct forces do apply to the mass (the gravitational pull from the Earth and the tension from the cable), we conclude that these two forces are themselves equal and opposite, i.e., that they compensate each other. However, these latter two forces are not the action and the reaction of each other as the forces are not of the same nature.
• To verify the correct interpretation of these concepts, let's replace the cable by a spring, and consider the same system initially at rest (again with respect to the ceiling of the laboratory): the same considerations apply. However, if this system is then perturbed (e.g., the mass is given a slight kick upwards or downwards, say), the mass starts to oscillate up and down. Because of these accelerations (and subsequent decelerations), we conclude from Newton's second law that a net force is responsible for the observed change in velocity. Yet, the gravitational action and reaction remain the same, since the masses involved have not changed, and the distance between the center of mass of the object and the center of mass of the Earth is modified so slightly that any variation in the gravitational force is immeasurably small. What has occurred is that we now have a dynamic system where the (constant) gravitational force on the mass is temporarily out of balance with the (variable) tension in the spring. The latter changes intensity and direction in time (at a frequency that is related to the strength of the spring), depending (in first approximation, and for small perturbations) on the deviation of the length of the spring with respect to its natural length (i.e., in the absence of a mass).

Examples of common misunderstandings

• Newton's third law is frequently stated in a simplistic but incomplete or incorrect manner through statements such as
Action and reaction are equal and opposite
To every action there is an equal and opposite reaction

These statements fail to make it clear that the action and reaction apply to different bodies. Also, it is not because two forces happen to be equal in magnitude and opposite in direction that they automatically form an action-reaction pair in the sense of Newton's Third Law.
• Action and reaction are often confused with the issue of equilibrium. For example, consider the following statement:
A book standing still on a table is at rest because its weight, a force pulling it downwards, is balanced by the equal and opposite reaction of the table, a force pushing it upwards.

This statement is misleading in that it suggests that the force exerted by the table on the book is the reaction associated with the book's weight. This is not the case, since the two forces are different in nature and are both applied to the book; one cannot be the reaction to the other, since they must apply to different bodies. In fact the force exerted by the table can be seen as the reaction to the contact force
Contact force
In physics, a contact force is a force that acts at the point of contact between two objects, in contrast to body forces. Contact forces are described by Newton's laws of motion, as with all other forces in dynamics....

exerted by the book on the table, which in turn is equal to the book's weight
Weight
In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude , often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus:...

.
• Another very common mistake is to state that
The centrifugal force that an object experiences is the reaction to the centripetal force on that object.

Clearly, if an object were simultaneously subject to both a centripetal force
Centripetal force
Centripetal force is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens...

and an equal and opposite reactive centrifugal force
Reactive centrifugal force
In classical mechanics, reactive centrifugal force is the reaction paired with centripetal force. A mass undergoing circular motion constantly accelerates toward the axis of rotation. This centripetal acceleration is caused by a force exerted on the mass by some other object. In accordance with...

, the resultant force
Net force
In physics, net force is the total force acting on an object. It is calculated by vector addition of all forces that are actually acting on that object. Net force has the same effect on the translational motion of the object as all actual forces taken together...

would vanish and the object could not experience a circular motion. The centrifugal force is sometimes called a fictitious force
Fictitious force
A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial frame of reference, such as a rotating reference frame....

or pseudo force, to underscore the fact that such a force only appears when calculations or measurements are conducted in non-inertial reference frames.
However, the term centrifugal force can also be used, in a different meaning, to denote the reaction force to the centripetal force. It is correct to state, for example: A car driving in a curve exerts a centrifugal force on the road.
• A particularly subtle common mistake is to confuse the forces that cause action and reaction with the actual action and reaction.

This mistake comes about partly because the very definition of force is all about a mass experiencing an acceleration, and there is an assumption that an object's entire mass is always the entity that is accelerating. Actually, though, when an object experiences a common impact-type of force, at the instant the force is applied, only the atoms and molecules at the surface of the object begin to accelerate. These push on neighboring atoms and molecules, and a mechanical wave of force propagates through the body of the object at the speed of sound in the substance of the object. The well-understood field of seismology
Seismology
Seismology is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other planet-like bodies. The field also includes studies of earthquake effects, such as tsunamis as well as diverse seismic sources such as volcanic, tectonic, oceanic,...

is full of information about forces traveling through a number of different substances at the different speed-of-sound in each substance, and the time it takes for distant things to be affected by those forces. Naturally, since ordinary objects are much smaller than the Earth, they become wholly affected by applied forces much more quickly -- typically, the entire mass of an ordinary object experiences an applied force in a thousandth of a second or less (just divide speed of sound
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....

in substance, into longest-physical-dimension of object) --which makes it easy to assume (especially in eras before modern instrumentation existed) that the whole mass of the object can instantly experience the force. From this description, however, it should be obvious that during the time that the wave of force propagates through an object, only part of the mass of the object is accelerating, not all of it. Another result of that description is that when two significantly different masses interact, even though the force between them, which causes action and reaction, happens perfectly simultaneously, the two masses may not fully respond/accelerate/act/react simultaneously. An actual example of this is a weapon under development, known as a "rarefaction wave gun". It is possible to open the breech of a cannon during firing (at just the right moment!) such that the recoil is reduced, but the velocity of the shell is not, because, by the time it takes the rarefaction-wave-of-reduced-gas-pressure/force to traverse the distance between the breech and the shell, the shell will have exited the gun barrel and is beyond reach of its effects. Another variant on the theme is Valve float
Valve float
Valve float is an adverse condition which occurs when the poppet valves on an internal combustion engine valvetrain do not remain in contact with the camshaft lobe during the valve closure phase of the cam lobe profile...

, in which the force applied by a spring, which can move a valve in an internal combustion engine, doesn't affect the whole valve quickly enough to keep it in contact with a rapidly rotating cam.

• Ground reaction force
Ground reaction force
In physics, and in particular in biomechanics, the ground reaction force is the force exerted by the ground on a body in contact with it.For example, a person standing on the ground exerts a contact force on it and at the same time an equal and opposite ground reaction force is exerted by the...

• Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

• Ibn Bajjah
Ibn Bajjah
Abū-Bakr Muhammad ibn Yahya ibn al-Sāyigh , known as Ibn Bājjah , was an Andalusian polymath: an astronomer, logician, musician, philosopher, physician, physicist, psychologist, botanist, poet and scientist. He was known in the West by his Latinized name, Avempace...

• Reaction engine
Reaction engine
A reaction engine is an engine or motor which provides propulsion by expelling reaction mass, in accordance with Newton's third law of motion...

/jet engine
Jet engine
A jet engine is a reaction engine that discharges a fast moving jet to generate thrust by jet propulsion and in accordance with Newton's laws of motion. This broad definition of jet engines includes turbojets, turbofans, rockets, ramjets, pulse jets...