From Wikiversity
Jump to: navigation, search


Newton's laws of motion[edit]

cogito ergo sum
resisto ergo sum
resisto et persisto

(1) I gets steady, when
(2) U exerts on I, then
(3) I reacts on U, end.

w: Newton's laws of motion[edit]

Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. They have been expressed in several different ways, over nearly three centuries, and can be summarised as follows.

Law I
Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.
Law II
The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.
To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
First law
When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force. [ha 1]
Second law
The vector sum of the external forces F on an object is equal to the mass m of that object multiplied by the acceleration vector a of the object: F = ma. [ha 2]
Third law
When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body. [ha 3] [ha 4]

w: Inertia [edit]

Inertia is the resistance of any physical object to any change in its state of motion (this includes changes to its speed, direction or state of rest). It is the tendency of objects to keep moving in a straight line at constant velocity. The principle of inertia is one of the fundamental principles of classical physics that are used to describe the motion of objects and how they are affected by applied forces. Inertia comes from the Latin word, iners, meaning idle, sluggish. Inertia is one of the primary manifestations of mass, which is a quantitative property of physical systems. Isaac Newton defined inertia as his first law in his Philosophiæ Naturalis Principia Mathematica, which states:

The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.

In common usage, the term "inertia" may refer to an object's "amount of resistance to change in velocity" (which is quantified by its mass), or sometimes to its momentum, depending on the context. The term "inertia" is more properly understood as shorthand for "the principle of inertia" as described by Newton in his First Law of Motion: that an object not subject to any net external force moves at a constant velocity. Thus, an object will continue moving at its current velocity until some force causes its speed or direction to change.

On the surface of the Earth, inertia is often masked by the effects of friction and air resistance, both of which tend to decrease the speed of moving objects (commonly to the point of rest), and gravity. This misled the philosopher Aristotle, to believe that objects would move only as long as force was applied to them: [body] stops when the force which is pushing the travelling object has no longer power to push it along...

w: Force[edit]

In physics, a force is any interaction that, when unopposed, will change the motion of an object.[1] In other words, a force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described by intuitive concepts such as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F.

The original form of Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. If the mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.

Related concepts to force include: thrust, which increases the velocity of an object; drag, which decreases the velocity of an object; and torque, which produces changes in rotational speed of an object. In an extended body, each part usually applies forces on the adjacent parts; the distribution of such forces through the body is the so-called mechanical stress. Pressure is a simple type of stress. Stress usually causes deformation of solid materials, or flow in fluids.

See also

w: Reaction (physics)[edit]

w: Reaction (physics) #Gravitational force[edit]

The Moon in reaction (Quotation parodied:)

The Moon orbits around the Earth because the gravitational force exerted by the Earth on the Moon, the action, serves as the centripetal force that maintains the Moon in the neighborhood of the Earth. Simultaneously, the Moon exerts a gravitational attraction on the Earth, the reaction, which has the same amplitude as the action and an opposite direction (in this case, pulling the Earth towards the Moon). Since the Earth's mass is very much larger than the Moon's, it does not appear to be reacting to the pull of the Moon, but in fact it does.

The Sun in action (Quotation follows:)

The Earth orbits around the Sun because the gravitational force exerted by the Sun on the Earth, the action, serves as the centripetal force 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 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.

Schematic of the lunar portion of earth's tides showing (exaggerated) high tides at the sublunar and antipodal points for the hypothetical case of an ocean of constant depth with no land. [...]
It may properly apply Newton's third law to say that the earth's pull is an action while the moon's pull is the reaction, as explained in the left quotation above. However, that may not be the whole story of action and reaction in this earth-moon case.
The rising tide shows up the moon's pull, whereas the ebbing shows up the restoring force toward the initial, inertial, steady state, relaxing the earth's reaction to the moon's pull that is an action!
The earth's pull as an action exerts a centripetal force on the moon, causing the moon's reactive centrifugal force, that is, not fictitious force but practical reaction. The moon is to resist the earth's pull to persist in a steady state, and vice versa.
"A pendulum is a weight suspended from a pivot." Both are connected by a rod or string. Via the medium, the weight acts its weight on the pivot, pulling it down. In response, the pivot reacts an equal and opposite force on itself (above all), pulling up the weight (after all) as well as itself, so as to keep itself from being pulled down, even broken down, to keep itself steady, as per Newton's law of inertia.

w: Tide[edit]

Diagram showing a circle with closely spaced arrows pointing away from the reader on the left and right sides, while pointing towards the user on the top and bottom.
The lunar gravity differential field at the Earth's surface is known as the tide-generating force. This is the primary mechanism that drives tidal action and explains two equipotential tidal bulges, accounting for two daily high waters.
This oval, with only one axis of symmetry, resembles a chicken egg.
[ patched from w: Oval ]
Why is the tidal Earth not egg-shaped, bulging toward the Moon (say, on the right)?

The ocean's surface is closely approximated by an equipotential surface, (ignoring ocean currents) commonly referred to as the geoid. Since the gravitational force is equal to the potential's gradient, there are no tangential forces on such a surface, and the ocean surface is thus in gravitational equilibrium. Now consider the effect of massive external bodies such as the Moon and Sun. These bodies have strong gravitational fields that diminish with distance and act to alter the shape of an equipotential surface on the Earth. This deformation has a fixed spatial orientation relative to the influencing body. The Earth's rotation relative to this shape causes the daily tidal cycle. Gravitational forces follow an inverse-square law (force is inversely proportional to the square of the distance), but tidal forces are inversely proportional to the cube of the distance. The ocean surface moves because of the changing tidal equipotential, rising when the tidal potential is high, which occurs on the parts of the Earth nearest to and furthest from the Moon. When the tidal equipotential changes, the ocean surface is no longer aligned with it, so the apparent direction of the vertical shifts. The surface then experiences a down slope, in the direction that the equipotential has risen.

Laplace's tidal equations

Ocean depths are much smaller than their horizontal extent. Thus, the response to tidal forcing can be modelled using the Laplace tidal equations which incorporate the following features:

  1. The vertical (or radial) velocity is negligible, and there is no vertical shear--this is a sheet flow.
  2. The forcing is only horizontal (tangential).
  3. The Coriolis effect appears as an inertial force (fictitious) acting laterally to the direction of flow and proportional to velocity.
  4. The surface height's rate of change is proportional to the negative divergence of velocity multiplied by the depth. As the horizontal velocity stretches or compresses the ocean as a sheet, the volume thins or thickens, respectively.


The Coriolis effect (inertial force) steers flows moving towards the equator to the west and flows moving away from the equator toward the east, allowing coastally trapped waves. Finally, a dissipation term can be added which is an analog to viscosity.

w: Tidal force[edit]

Figure 2: The Moon's gravity differential field at the surface of the Earth is known (along with another and weaker differential effect due to the Sun) as the Tide Generating Force. This is the primary mechanism driving tidal action, explaining two tidal equipotential bulges, and accounting for two high tides per day. In this figure, the Earth is the central blue circle while the Moon is far off to the right. The outward direction of the arrows on the right and left indicates that where the Moon is overhead (or at the nadir) its perturbing force opposes that between the earth and ocean.

The tidal force is a secondary effect of the force of gravity and is responsible for the tides. It arises because the gravitational force exerted by one body on another is not constant across it; the nearest side is attracted more strongly than the farthest side. Thus, the tidal force is differential. Consider the gravitational attraction of the moon on the oceans nearest to the moon, the solid Earth and the oceans farthest from the moon. There is a mutual attraction between the moon and the solid earth which can be considered to act on its centre of mass. However, the near oceans are more strongly attracted and, since they are fluid, they approach the moon slightly, causing a high tide. The far oceans are attracted less. The attraction on the far-side oceans could be expected to cause a low tide but since the solid earth is attracted (accelerated) more strongly towards the moon, there is a relative acceleration of those waters in the outwards direction. Viewing the Earth as a whole, we see that all its mass experiences a mutual attraction with that of the moon but the near oceans more so than the far oceans, leading to a separation of the two.

In a more general usage in celestial mechanics, the expression 'tidal force' can refer to a situation in which a body or material (for example, tidal water) is mainly under the gravitational influence of a second body (for example, the Earth), but is also perturbed by the gravitational effects of a third body (for example, the Moon). The perturbing force is sometimes in such cases called a tidal force (for example, the perturbing force on the Moon): it is the difference between the force exerted by the third body on the second and the force exerted by the third body on the first.


When a body (body 1) is acted on by the gravity of another body (body 2), the field can vary significantly on body 1 between the side of the body facing body 2 and the side facing away from body 2. Figure 2 shows the differential force of gravity on a spherical body (body 1) exerted by another body (body 2). These so-called tidal forces cause strains on both bodies and may distort them or even, in extreme cases, break one or the other apart.[2] The Roche limit is the distance from a planet at which tidal effects would cause an object to disintegrate because the differential force of gravity from the planet overcomes the attraction of the parts of the object for one another. These strains would not occur if the gravitational field were uniform, because a uniform field only causes the entire body to accelerate together in the same direction and at the same rate.

Restoring force[edit]

w: Restoring force

Restoring force, in a physics context, is a force that gives rise to an equilibrium in a physical system. If the system is perturbed away from the equilibrium, the restoring force will tend to bring the system back toward equilibrium. The restoring force is a function only of position of the mass or particle. It is always directed back toward the equilibrium position of the system. The restoring force is often referred to in simple harmonic motion.

An example is the action of a spring. An idealized spring exerts a force that is proportional to the amount of deformation of the spring from its equilibrium length, exerted in a direction to oppose the deformation. Pulling the spring to a greater length causes it to exert a force that brings the spring back toward its equilibrium length. The amount of force can be determined by multiplying the spring constant of the spring by the amount of stretch.

Another example is of a pendulum. When the pendulum is not swinging all the forces acting on the pendulum are in equilibrium. The force due to gravity and the mass of the object at the end of the pendulum is equal to the tension in the string holding that object up. When a pendulum is put in motion the place of equilibrium is at the bottom of the swing, the place where the pendulum rests. When the pendulum is at the top of its swing the force bringing the pendulum back down to this midpoint is gravity. As a result gravity can be seen as the restoring force in this case.


w: Spring (device) #Theory[edit]

In classical physics, a spring can be seen as a device that stores potential energy, specifically elastic potential energy, by straining the bonds between the atoms of an elastic material.

Hooke's law of elasticity states that the extension of an elastic rod (its distended length minus its relaxed length) is linearly proportional to its tension, the force used to stretch it. Similarly, the contraction (negative extension) is proportional to the compression (negative tension).

This law actually holds only approximately, and only when the deformation (extension or contraction) is small compared to the rod's overall length. For deformations beyond the elastic limit, atomic bonds get broken or rearranged, and a spring may snap, buckle, or permanently deform. Many materials have no clearly defined elastic limit, and Hooke's law can not be meaningfully applied to these materials. Moreover, for the superelastic materials, the linear relationship between force and displacement is appropriate only in the low-strain region.

Hooke's law is a mathematical consequence of the fact that the potential energy of the rod is a minimum when it has its relaxed length. [...]


w: Pendulum[edit]

A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force combined with the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum, and also to a slight degree on the amplitude, the width of the pendulum's swing.


The simple gravity pendulum is an idealized mathematical model of a pendulum. This is a weight (or bob) on the end of a massless cord suspended from a pivot, without friction. When given an initial push, it will swing back and forth at a constant amplitude. Real pendulums are subject to friction and air drag, so the amplitude of their swings declines.


Rolling resistance[edit]

w: Friction #Rolling resistance

Rolling resistance is the force that resists the rolling of a wheel or other circular object along a surface caused by deformations in the object and/or surface. Generally the force of rolling resistance is less than that associated with kinetic friction. [...] One of the most common examples of rolling resistance is the movement of motor vehicle tires on a road, a process which generates heat and sound as by-products.

Reaction (physics)[edit]

w: Reaction (physics)

As described by the third of Newton's laws of motion of classical mechanics, all forces occur in pairs such that if one object exerts a force on another object, then the second object exerts an equal and opposite reaction force on the first.[3] The third law is also more generally stated as: "To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts."[4] The attribution of which of the two forces is the action and which is the reaction is arbitrary. Either of the two can be considered the action, while the other is its associated reaction.


Interaction with ground[edit]

When something is exerting force on the ground, the ground will push back with equal force in the opposite direction. In certain fields of applied physics, such as biomechanics, this force by the ground is called 'ground reaction force'; the force by the object on the ground is viewed as the 'action'.

When someone wants to jump, he or she exerts additional downward force on the ground ('action'). Simultaneously, the ground exerts upward force on the person ('reaction'). If this upward force is greater than the person's weight, this will result in upward acceleration. When these forces are perpendicular to the ground, they are also called a normal force.

Likewise, the spinning wheels of a vehicle attempt to slide backward across the ground. If the ground is not too slippery, this results in a pair of friction forces: the 'action' by the wheel on the ground in backward direction, and the 'reaction' by the ground on the wheel in forward direction. This forward force propels the vehicle.

Gravitational forces[edit]

The Earth orbits around the Sun because the gravitational force exerted by the Sun on the Earth, the action, serves as the centripetal force 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 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 of the combined system.

Supported mass[edit]

Any mass on earth is pulled down by the gravitational force of the earth; this force is also called its weight. The corresponding 'reaction' is the gravitational force that mass exerts on the planet.

If the object is supported so that it remains at rest, for instance by a cable from which it is hanging, or by a surface underneath, or by a liquid on which it is floating, there is also a support force in upward direction (tension force, normal force, buoyant force, respectively). This support force is an 'equal and opposite' force; we know this not because of Newton's Third Law, but because the object remains at rest, so that the forces must be balanced.

To this support force there is also a 'reaction': the object pulls down on the supporting cable, or pushes down on the supporting surface or liquid. In this case, there are therefore four forces of equal magnitude:

  • F1. gravitational force by earth on object (downward)
  • F2. gravitational force by object on earth (upward)
  • F3. force by support on object (upward)
  • F4. force by object on support (downward)

Forces F1 and F2 are equal because of Newton's Third Law; the same is true for forces F3 and F4. Forces F1 and F3 are only equal if the object is in equilibrium, and no other forces are applied. This has nothing to do with Newton's Third Law.

Mass on a spring[edit]

If a mass is hanging from a spring, the same considerations apply as before. 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. The gravitational force pulling down on the mass is no longer equal to the upward elastic force of the spring. In the terminology of the previous section, F1 and F3 are no longer equal.

However, it is still true that F1 = F2 and F3 = F4, as this is required by Newton's Third Law.

Causal misinterpretation[edit]

The terms 'action' and 'reaction' have the unfortunate suggestion of causality, as if the 'action' is the cause and 'reaction' is the effect. It is therefore easy to think of the second force as being there because of the first, and even happening some time after the first. This is incorrect; the forces are perfectly simultaneous, and are there for the same reason.

When the forces are caused by a person's volition (e.g. a soccer player kicks a ball), this volitional cause often leads to an asymmetric interpretation, where the force by the player on the ball is considered the 'action' and the force by the ball on the player, the 'reaction'. But physically, the situation is symmetric. The forces on ball and player are both explained by their nearness, which results in a pair of contact forces (ultimately due to electric repulsion). That this nearness is caused by a decision of the player has no bearing on the physical analysis. As far as the physics is concerned, the labels 'action' and 'reaction' can be flipped.

'Equal and opposite'[edit]

One problem frequently observed by physics educators is that students tend to apply Newton's Third Law to pairs of 'equal and opposite' forces acting on the same object.[5][6] This is incorrect; the Third Law refers to forces on two different objects. [ha 5] For example, a book lying on a table is subject to a downward gravitational force (exerted by the earth) and to an upward normal force by the table. Since the book is not accelerating, these forces must be exactly balanced, according to Newton's First or Second law. They are therefore 'equal and opposite'. However, these forces are not always equally strong; they will be different if the book is pushed down by a third force, or if the table is slanted, or if the table-and-book system is in an accelerating elevator. The case of three or more forces is covered by considering the sum of all forces.

A possible cause of this problem is that the Third Law is often stated in an abbreviated form: For every action there is an equal and opposite reaction, without the details, namely that these forces act on two different objects. Moreover, there is a causal connection between the weight of something and the normal force: if an object had no weight, it would not experience support force from the table, and the weight dictates how strong the support force will be. This causal relationship is not due to the Third Law but to other physical relations in the system.

Centripetal and centrifugal force[edit]

Another common mistake[original research?]

is to state that

The centrifugal force that an object experiences is the reaction to the centripetal force on that object.

If an object were simultaneously subject to both a centripetal force and an equal and opposite centrifugal force, the resultant force would vanish and the object could not experience a circular motion. The centrifugal force is sometimes called a fictitious force or pseudo force, to underscore the fact that such a force only appears when calculations or measurements are conducted in non-inertial reference frames.

See also[edit]


  • Feynman, R. P., Leighton and Sands (1970) The Feynman Lectures on Physics, Volume 1, Addison Wesley Longman, ISBN 0-201-02115-3.
  • Resnick, R. and D. Halliday (1966) Physics, Part 1, John Wiley & Sons, New York, 646 pp + Appendices.
  • Warren, J. W. (1965) The Teaching of Physics, Butterworths, London,130 pp.

User:KYPark/Centrifugal force

User:KYPark/Reactive centrifugal force

User:KYPark/Fictitious force



  1. The First law is looking to an initial, inertial, steady state before any change, hence the contrast to the Third law after some change.
  2. The Second law sounds like a definition rather than a law. Should definitions were worth a law, too many laws would dictate to us.
  3. The Third law is something after any change to complement and supplement the First law before any change. Anyway, this last law seems most problematic! Perhaps ill oriented, from the beginning.
  4. A universal truth may be that everything is to resist to persist. Whatever law says so?
  5. Suppose you either elongate or compress a coil spring with two hands. Then a pair of two 'equal and opposite' forces act on just one thing by your hands, one of which should be 'action' while the other 'reaction', regardless of which is first. In this very case of not 'two things' but 'one thing', acted and reacted upon, should we never subscribe to Newton's 3rd law, as originally built on 'two things'?

    Although the resulting 'net force' may be zero-sum, cancelling each other, the said pair of forces did work indeed anyway by making the spring either longer or shorter, while innately building up a definite elasticity, that is, restoring force or energy hidden within, as hard to prove as Yin. Yet zero-sum games work!

    Perhaps more fortunate is the above case that there is anyway something to be acted and reacted upon. In contrast, suppose a rocket flying in a gravity-free state. There is nothing to be acted and reacted upon. The rocket acts on nothing, but just flies opposite to its jet.

    Who pushes it? No one but just the reaction (as Yin) to its jet action (as Yang)!

  1. Nave, C. R. (2014). "Force". Hyperphysics. Dept. of Physics and Astronomy, Georgia State University. Retrieved 15 August 2014. 
  2. R Penrose (1999). The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford University Press. p. 264. ISBN 0-19-286198-0. 
  3. Taylor, John R. (2005). Classical Mechanics. University Science Books. pp. 17–18. ISBN 9781891389221. 
  4. This translation of the third law and the commentary following it can be found in the "Principia" on page 20 of volume 1 of the 1729 translation.
  5. Colin Terry and George Jones (1986). "Alternative frameworks: Newton's third law and conceptual change". European Journal of Science Education 8 (3): 291–298. doi:10.1080/0140528860080305. Retrieved 2013-10-26. "This report highlights some of the difficulties that children experience with Newton's third law." 
  6. Cornelis Hellingman (1992). "Newton's Third Law Revisited". Physics Education 27: 112–115. doi:10.1088/0031-9120/27/2/011. Retrieved 2013-10-26. "... following question in writing: Newton’s third law speaks about ‘action’ and ‘reaction’. Imagine a bottle of wine standing on a table. If the gravitational force that attracts the bottle is called the action, what force is the reaction to this force according to Newton’s third law? The answer most frequently given was: ‘The normal force the table exerts on the bottle’."