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The definition of force in classical mechanics is quite simple and clear-force is the action of objects on objects, yes, quite simple and clear! Therefore, people think that only two or more objects are qualified to talk about force, and when it comes to force, there must be objects that exert force and objects that are stressed, which seems to be consistent with people's life practice.
However, when people sit in the car and take the car as the frame of reference, we find that the objects in the car can actually accelerate for no reason. There seems to be a force acting on these objects. What power is this? What are its properties? What is the object of force? No matter how hard we try, we can't find the object of this force. In order to find out the reason, we got off the bus and looked at it again on the ground with the ground as the reference system. At this time, we suddenly realized that once the car accelerates, the object on the car will accelerate relative to the car, and the object will not move at all, but will remain at rest, and the object will not be stressed. Of course, we can't find the object that exerts force. It can be seen that observing the movement of objects in different reference systems will get completely different results!
Therefore, people classify reference systems. Any reference frame to which Newton's second law can be applied is called inertial reference frame, and conversely, any reference frame to which Newton's second law cannot be applied is called non-inertial reference frame. Whether Newton's second law is applicable or not, the factor we consider is actually the condition of force generation. If the generation of force is conditional, it must conform to Newton's second law. Through summary, it is found that all reference frames that are stationary or moving in a straight line at a constant speed relative to the ground are inertial reference frames, while those that are moving at a variable speed relative to the ground are non-inertial reference frames. Among many inertial reference systems, the inertial reference system that is stationary relative to the ground has special advantages and is called absolute inertial reference system.
People have discussed a lot about inertial frame of reference and non-inertial frame of reference. An object seems to be accelerating under the force of a non-inertial system, but no object can be found to apply the force. In order to satisfy Newton's second law, people assume that an object is acted by a force, which is determined by the product of its mass and acceleration. However, because no object can be found to exert this force, people think that this force is not a real force, but a fictional force, and call this force "inertial force".
Obviously, the magnitude of "inertial force" depends on the acceleration of the object, and the acceleration of the object actually depends on the acceleration of the non-inertial reference frame relative to the inertial reference frame. It can be seen that when classical mechanics discusses the non-inertial system, it is inseparable from the inertial system for a moment, and it is difficult to move without it. As a result, classical mechanics finally fell into the trap of frame of reference cycle!
Rotating non-inertial reference system and Coriolis inertial force
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The reference frame of variable speed movement relative to the inertial reference frame is a non-inertial reference frame, and the objects in the non-inertial reference frame will be subjected to inertial force. Rotation is also a kind of variable speed movement, and it is also a kind of variable speed movement that is often seen. If an object rotating relative to the ground is taken as a frame of reference, it will be subjected to two kinds of inertial forces-centrifugal inertial force and Coriolis inertial force. In this paper, only the Coriolis inertia force is discussed correspondingly, and the centrifugal inertia force is discussed again in the article on the reference frame.
For Coriolis force, for various reasons, the author can't consult and extract the most original literature about Coriolis force. This article is an excerpt from the 65438th edition of Fundamentals of Mechanics (edited by Qi Anshen and Du Chanying, published by Higher Education Press in February, a trial textbook for colleges and universities, 1982+ 1).
As mentioned above, when a particle is stationary in a reference frame rotating at a constant speed, it will be observed that the particle is subjected to centrifugal inertia force. If a particle moves relative to a reference frame rotating at a constant speed, it may be subjected to another inertial force, namely Coriolis force.
See figure 2.35. The horizontal smoothness can rotate around the vertical axis o ... Assuming that the disk is stationary and the resultant force is zero, the ball moves from disk A to the radius of bearing B at a constant speed. No matter from the point of view of the disk, the motion state of the ball is the same. If the disk rotates at a constant angular velocity, the ball at point A on the disk has only the same linear velocity as point A. After a short period of time, it can be approximately considered that the ball moves from point A on the original disk to point C where A is located. As shown in Figure 2.35(b) (note that the angle is exaggerated for clarity). Now when the disc rotates, the ball will participate in the above two kinds of uniform linear motions from A to B and from A to C relative to the inertial system, and the ball should reach point D in Figure 2.35(c). At the same time, the original radius of the ball has turned a certain angle, from AB to CD'. Seen from the disc, the ball can't stay in its original position.
If there are grooves with smooth inner walls along the radial direction on the disk, the situation will be different. The ball at point A in the groove still has the above-mentioned velocities along AB and AC relative to the inertial system, but at this time, due to the constraint of the groove, after a short period of time, the ball will reach point D', thus making up for the displacement from point D to point D', as shown in Figure 2.36(a). It can be seen that in this movement, the ball will inevitably get some jerk near the radius perpendicular to inertia to make up for the displacement DD'.
If the ball moves at a uniform speed along the vertical direction of the radius, and the magnitude of the additional acceleration indicates the time when the ball moves from A to D', then the angular displacement of the disc is zero in time. Considering that the ball moves at a uniform speed along the groove, it indicates its grooving speed relative to the disc, so it is compared with the above formula.
This additional acceleration is observed in the inertial system, which is called Coriolis acceleration and is produced by some relative interaction force. The ball with mass m is in the groove, and this force can only be the elastic force exerted by the groove edge, which should be perpendicular to the groove and equal in size, as shown in Figure 2.36(a).
From the non-inertial system of the disk, the ball just moves in a straight line at a uniform speed along the groove. According to Newton's second law, the resultant force on the ball should be zero. But the ball has been subjected to the force just mentioned, so there must be a balance between inertia force and force, but in the opposite direction.
Seven laws of physical properties and Lin San's laws in non-inertial system
The author discusses the motion characteristics of objects in the field environment in many articles, and summarizes the seven laws of physical characteristics and Lin San's laws on this basis.
In the density gradient field of free particles, a free object will make an attribute motion determined by the density gradient, and the attribute acceleration is proportional to the density gradient, which is equal to the square of the propagation speed of shear wave in this particle, that is, the density of free particles and the density of similar free particles in the object. This is the zeroth law of physical properties.
The velocity change of a free particle at a fixed point in space produces a velocity change rate field at a certain point, and the acceleration of a free object that a free particle can freely penetrate in this field depends on the velocity change of the free particle at the position of the object. This is the first law of physical properties.
There is a velocity curl field of free particles in space, and a freely moving object will make an attribute motion determined by the velocity curl of space particles and the velocity of its object. Attribute acceleration is directly proportional to the velocity curl of space particles and the velocity of objects respectively. This is the second law of physical properties.
In the temperature gradient field of free atoms and molecules, a free object will make an attribute motion determined by the temperature gradient, and the attribute acceleration is proportional to the temperature gradient. This is the third law of physical properties.
In the electron density gradient field, the free charge will make an attribute motion determined by the density gradient, and the attribute acceleration is proportional to the density gradient. For charge, this field is Coulomb electric field or voltage distribution electric field, and the electric field intensity is 0. This is the fourth law of physical properties.
The acceleration potential of free charge in subspace depends on the time change rate of charge velocity. This is Lin's electrostatic field with a field strength of. This is the fifth law of physical properties.
The attribute acceleration potential of free-moving charge will be determined by the velocity curl of electrons and the motion speed of charge. This is a dynamic Lin's electric field with a field strength of. This is the sixth law of physical properties.
"Force" is a reflection of the degree of environmental imbalance, and an object is bound to accelerate in an unbalanced environment. "Force" is equal to the product of the mass of an object and its attribute acceleration, and it is an intermediate physical quantity to study the relationship between the degree of environmental imbalance and the attribute acceleration of an object in the corresponding environment. The author calls this definition the zeroth law of Lin Haibing.
All objects are always in equilibrium in a balanced environment until the environment changes from equilibrium to imbalance, forcing objects to change their original equilibrium state. This is Lin Haibing's first law.
All objects are always accelerating in an unbalanced environment, and their acceleration depends on the degree of imbalance in various environments. This is Lin Haibing's second law.
In the above law, the author uses the resistance velocity vector to represent the motion velocity of environmental particles.
4 The essence of Coriolis acceleration
People think that Coriolis acceleration is the result of non-inertial force, but it is not. In fact, this is only the motion property of matter in the medium-speed curl, which is described by the second law of physical properties.
The reason for its formation is very simple-if the disk rotates counterclockwise relative to the ground, then when the disk is used as the reference system, dark matter neutrons rotate clockwise at the same angular velocity, forming a certain velocity curl inside the reference system. We can calculate curl, which is the angular velocity vector of neutron rotating in the disk reference system. According to the second law of physical properties, the acceleration of an object in such a frame of reference is, that is, the speed of the object in a disk frame of reference. This is the Coriolis acceleration.
Therefore, in such an inertial system, an object may be subjected to two environmental attribute forces-Coriolis force and centrifugal force, and the resultant force is.
Additional gravitational field in non-inertial reference frame
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Considering the small celestial bodies falling to the earth at high altitude, simplified as not considering the influence of air and earth rotation, then choosing the earth and small celestial bodies as reference frames respectively are:
Take the earth as the reference system: because the earth is approximately the inertial system, small objects do free fall, and the kinetic energy increases when they reach the ground. Its kinetic energy is transformed from potential energy, and the conservation of energy holds.
Take a small object as the reference system: the small object is a non-inertial system. According to the general theory of relativity, there is an additional gravitational field, which points upwards. Under the action of the additional gravitational field, the earth accelerates along the direction of the additional gravitational field, and the additional gravitational field does work on the earth, and the kinetic energy of the earth keeps increasing until it falls on a small object as a reference system. The additional gravitational field acting on the earth increases the kinetic energy of the earth. Where does the energy of the additional gravitational field come from and how to explain it by energy conservation?
The same problem exists for rockets launched vertically upward as a reference system.
If free fall is a special case, there is no additional field.
Then, if the horizontally accelerating car is taken as the reference frame, there should be an additional field. Then you can observe that the earth is accelerating backwards. In this frame of reference, what energy is the incremental kinetic energy of the earth converted from?
Of course, when the earth is taken as the frame of reference, the kinetic energy increment of the car is supplied by the engine.