Non-inertial frame of reference: definition, examples

All reference systems are divided into inertial and non-inertial. The inertial reference system underlies Newton’s mechanics. It characterizes a uniform rectilinear motion and state of rest. The non-inertial frame of reference is associated with accelerated motion along a different trajectory. This movement is defined in relation to inertial reference systems. The non-inertial frame of reference is associated with such effects as inertial force, centrifugal force, and Coriolis force.

All these processes arise as a result of movement, and not the interaction between the bodies. Newton's laws in non-inertial reference systems often do not work. In such cases, amendments to the classical laws of mechanics are added. Forces due to non-inertial motion are taken into account when developing technical products and mechanisms, including those where rotation is present. In life, we encounter them, moving in an elevator, riding on the carousel, watching the weather and the flow of rivers. They are taken into account when calculating the motion of spacecraft.

non-inertial reference system

Inertial and non-inertial reference systems

Inertial reference systems are not always suitable for describing the movement of bodies. In physics, there are 2 types of reference systems: inertial and non-inertial reference systems. According to the mechanics of Newton, any body can be in a state of rest or a uniform and rectilinear motion, with the exception of cases when an external influence is exerted on the body. This uniform motion is called inertial motion.

Inertial motion (inertial reference systems) forms the basis of Newton's mechanics and the works of Galileo. If stars are considered to be fixed objects (which is actually not quite the case), then any objects moving relative to them evenly and straightforwardly will form inertial reference systems.

inertial and non-inertial reference systems

Unlike inertial reference systems, a non-inertial system moves in relation to the specified one with a certain acceleration. At the same time, the use of Newton's laws requires additional variables, otherwise they will inadequately describe the system. To answer the question, which reference systems are called non-inertial, it is worth considering an example of a non-inertial movement.This movement is the rotation of our and other planets.

Motion in non-inertial reference systems

Copernicus was the first to show how difficult a movement can be if several forces participate in it. Before him, it was believed that the Earth moves by itself, in accordance with Newton's laws, and therefore its motion is inertial. However, Copernicus proved that the Earth revolves around the Sun, that is, it makes an accelerated motion with respect to a conditionally stationary object, which a star can be.

motion in non-inertial reference systems

So, there are different reference systems. Non-inertial call only those where there is an accelerated motion, which is defined in relation to the inertial system.

Earth as a reference system

The non-inertial frame of reference, examples of whose existence can be found almost everywhere, is typical of bodies with a complex trajectory of motion. The Earth rotates around the Sun, which creates accelerated motion characteristic of non-inertial reference systems. However, in everyday practice, everything that we encounter on Earth is consistent with Newton's postulates. The thing is that the corrections for non-inertial motion for Earth-related reference systems are very small and do not play a big role for us.And the Newton equations for the same reason turn out to be in general fair.

inertial and non-inertial reference systems examples

Foucault's Pendulum

However, in some cases, no amendment is necessary. For example, the world famous Foucault pendulum in the cathedral of St. Petersburg not only performs linear oscillations, but also slowly turns. This rotation is due to the non-inertial motion of the Earth in outer space.

For the first time this became known in 1851 after the experiments of the French scientist L. Foucault. The experiment itself was conducted not in Petersburg, but in Paris, in a huge hall. The weight of the pendulum ball was about 30 kg, and the length of the connecting thread was as much as 67 meters.

In those cases when only Newton's formulas for the inertial reference system are not enough to describe the motion, they add the so-called inertia forces.

Properties of non-inertial reference system

The non-inertial reference system performs various movements relative to inertial. It can be forward movement, rotation, complex combined movements. Such a simplest example of a non-inertial frame of reference, such as an accelerated moving elevator, is also given in the literature.It is because of his accelerated movement that we feel how we are pressed down to the floor, or, on the contrary, a sensation is close to weightlessness. Newton's laws of mechanics cannot explain this phenomenon. If you follow the famous physicist, then at any moment the same force of gravity will act on a person in the elevator, which means that the sensations should be the same, however, in reality everything is different. Therefore, to the laws of Newton it is necessary to add additional force, which is called the force of inertia.

non-inertial inertial force systems

Force of inertia

The force of inertia is a real acting force, although it differs in nature from the forces associated with the interaction between bodies in space. It is taken into account in the development of technical structures and devices, and plays an important role in their work. Inertia forces are measured in various ways, for example, using a spring dynamometer. Non-inertial reference systems are not closed, since the inertia forces are considered external. The forces of inertia are objective physical factors and do not depend on the will and opinion of the observer.

Inertial and non-inertial reference systems,examples of manifestations which can be found in the textbooks of physics are the action of inertial force, centrifugal force, Coriolis force, the transfer of momentum from one body to another and others.

 forces in non-inertial reference systems

Movement in the elevator

Non-inertial reference systems, inertia forces well manifest themselves in accelerated ascent or descent. If the elevator moves upward with acceleration, then the resulting inertial force tends to press the person to the floor, and when braking, the body, on the contrary, begins to seem easier. In terms of manifestations, the force of inertia in this case is similar to gravity, but it has a completely different nature. Gravity is gravity, which is associated with the interaction between bodies.

what reference systems are called non-inertial

Centrifugal force

Forces in non-inertial reference systems can be centrifugal. It is necessary to introduce such a force for the same reason as the inertia force. A vivid example of the action of centrifugal forces - the rotation on the carousel. While the chair seeks to keep a person in its “orbit”, the force of inertia causes the body to press against the outer back of the chair. This confrontation is expressed in the appearance of such a phenomenon as centrifugal force.

Coriolis force

The effect of this force is well known from the example of the rotation of the Earth. You can call it by force only conditionally, since it is not. The essence of its action is that during rotation (for example, of the Earth) each point of a spherical body moves in a circle, while objects torn from the Earth ideally move in a straight line (such as a body freely flying in space). Since the line of latitude is a trajectory of rotation of points on the earth's surface, and has the form of a ring, any bodies separated from it and initially moving along this line, moving linearly, begin to deviate more and more from it towards lower latitudes.

Another option is when the body is launched in the meridional direction, but due to the rotation of the Earth, from the point of view of the earthly observer, the movement of the body will no longer be strictly meridional.

The Coriolis force has a great influence on the development of atmospheric processes. Under its influence, the water hits the eastern bank of the rivers flowing in the meridional direction harder, gradually eroding it, which leads to the appearance of cliffs. In the west, on the contrary, precipitation is deposited, so it is more gentle and often flooded with water during floods.True, this is not the only reason why one side of the river is higher than the other, but in many cases it is dominant.

The Coriolis force also has experimental evidence. It was obtained by the German physicist F. Reich. In the experiment, the bodies fell from a height of 158 m. A total of 106 such experiments were carried out. When a body fell, they deviated from a straight (from the point of view of an earthly observer) trajectory by approximately 30 mm.

Inertial reference systems and the theory of relativity

Einstein's special theory of relativity was created in relation to inertial reference systems. The so-called relativistic effects, according to this theory, should occur in the case of very high velocities of the body relative to the "stationary" observer. All formulas of the special theory of relativity are also written for uniform motion, typical of the inertial reference system. The first postulate of this theory asserts the equivalence of any inertial reference systems, i.e., the absence of special, dedicated systems is postulated.

However, this casts doubt on the possibility of checking relativistic effects (as well as the very fact of their existence), which led to the appearance of such phenomena as the twin paradox.Since the reference systems associated with the rocket and the Earth are fundamentally equal in rights, then the effects of time dilation in the pair Earth-Rocket will depend only on where the observer is. So, for an observer on a rocket, time on Earth should go slower, and for a person on our planet, on the contrary, it should go slower on a rocket. As a result, the twin remaining on Earth will see his brother arrive younger, and the one who was in the rocket, having flown in, should see younger than the one who remained on Earth. It is clear that this is physically impossible.

So, in order to observe relativistic effects, we need some kind of special, dedicated frame of reference. For example, it is assumed that we observe a relativistic increase in the lifetime of muons, if they move at near-light speed relative to the Earth. This means that the Earth should (moreover, without any alternative) possess the properties of a priority, basic reference system, which contradicts the first postulate of the SRT. Priority is possible only if the Earth is the center of the universe, which is consistent only with the primitive picture of the world and contrary to physics.

Non-inertial reference systems as an unsuccessful way to explain the twin paradox

Attempts to explain the priority of the "earthly" reference system do not hold water. Some scientists attribute this priority to the factor of inertia of one and non-inertiality of another system of reference. In this case, the reference system associated with an observer on Earth is considered inertial, despite the fact that in physical science it is officially recognized as non-inertial (Detlaf, Yavorsky, physics course, 2000). This is the first. The second is all the same principle of equality of any reference systems. So, if a spacecraft leaves the Earth with acceleration, then from the point of view of the observer on the ship itself, it is static, and the Earth, on the contrary, flies away from it with increasing speed.

It turns out that the Earth itself is a special reference system, or the observed effects have a different (non-relativistic) explanation. Perhaps the processes are associated with the peculiarities of the formulation or interpretation of experiments, or with other physical mechanisms of the observed phenomena.


Thus, non-inertial reference systems lead to the appearance of forces that have not found their place in the laws of Newtonian mechanics.When calculating for non-inertial systems, accounting for these forces is mandatory, including in the development of technical products.

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