What is Coriolis force? What are the applications?

Coriolis force in this paragraph is also called Coriolis force in some places, which is called Coriolis force for short. It is a description of the deviation of particles in a rotating system due to inertia relative to the linear motion of the rotating system. Understanding the Coriolis force of linear motion of particles in the rotating system of historical editing is based on Newtonian mechanics. 1835, French meteorologist Coriolis proposed that in order to describe the motion of a rotating system, an imaginary force should be introduced into the motion equation, which is Coriolis force. After the introduction of Coriolis force, people can deal with the equation of motion in the rotating system as simply as the equation of motion in the inertial system, which greatly simplifies the processing method of the rotating system. Because the earth where human beings live is a huge rotating system, Coriolis force has been successfully applied in the field of fluid movement. Coriolis force in physics The Coriolis force in this paragraph comes from the inertia of the object's motion. Particles moving in a straight line in a rotating system tend to move in the original direction due to inertia. However, because the system itself is rotating, the position of particles in the system will change after moving for a period of time. Observe its original moving direction from the perspective of rotating system.

As shown on the right, when a particle moves in a straight line relative to the inertial system, its trajectory is a curve relative to the rotational system. Based on the rotating system, we think that there is a force that drives the trajectory of particles to form a curve, and this force is Coriolis force.

According to the theory of Newtonian mechanics, taking the rotating system as the frame of reference, this tendency of linear motion of particles to deviate from the original direction is attributed to the action of an external force, which is Coriolis force. From the physical point of view, Coriolis force, like centrifugal force, is not a real force, but the embodiment of inertia in a non-inertial system.

The formula for calculating Coriolis force is as follows:

F=2m*v*ω

Where f is Coriolis force; M is the mass of the particle; V is the velocity of particles; ω is the angular velocity of the rotating system; * Represents the outer product symbol of two vectors. The influence of Coriolis force is edited in this paragraph 1 in the field of earth science.

Because of the existence of rotation, the earth is not an inertial system, but a rotating reference system, so the movement of particles on the ground is affected by Coriolis force. The geostrophic deflection force in the field of earth science is a component of Coriolis force along the surface of the earth. The geostrophic bias helps to explain some geographical phenomena, for example, one side of a river is often washed more seriously than the other.

2 Foucault pendulum

Swing can be regarded as reciprocating linear motion, and the swing on the earth will be affected by the rotation of the earth. As long as there is a certain angle between the direction of the pendulum and the direction of the angular velocity of the earth's rotation, the pendulum will be subjected to Coriolis force, which will produce a moment opposite to the direction of the earth's rotation, thus making the pendulum rotate. 185 1 year, French physicist Foucault predicted the existence of this phenomenon and proved it through experiments. He made a pendulum with a 67-meter-long steel wire rope and a 27-kilogram metal ball, embedded a pointer under the pendulum and hung the huge pendulum on the dome of the church. Experiments have confirmed that in the northern hemisphere, the pendulum will slowly rotate to the right. Because Foucault first proposed and completed this experiment, this experiment was named Foucault pendulum experiment.

Trade winds and monsoons

Different areas at different latitudes of the earth's surface receive different amounts of sunlight, which affects the flow of the atmosphere. A series of pressure zones are formed along the latitude of the earth's surface, such as the so-called polar high pressure zone, sub-polar low pressure zone and subtropical high pressure zone. Driven by the pressure difference of these gas belts, the air will move along the longitudinal direction, which can be regarded as the linear movement of particles in the rotating system, and the particles will be deflected by Coriolis force. It is not difficult to see from the formula of Coriolis force that the atmospheric airflow in the northern hemisphere will deflect to the right and the atmospheric airflow in the southern hemisphere will deflect to the left. Under the combined action of Coriolis force, atmospheric pressure difference and surface friction, the original north-south atmospheric flow will become northeast-southwest or southeast-northwest atmospheric flow.

With the change of seasons, the pressure belt along the latitude of the earth's surface will drift from north to south, so the wind direction in some places will change seasonally, which is called monsoon. Of course, this must also involve the difference in air pressure caused by the difference in specific heat between land and ocean.

Coriolis force makes the direction of monsoon shift to a certain extent, resulting in the east-west movement factor. Historically, wind-driven human navigation has largely concentrated in the latitude extension direction, and the existence of monsoon has created great convenience for human navigation, so it is also called trade wind.

4 tropical cyclone

The direction of toilet launching is related to Coriolis force, and the formation of tropical cyclone (called typhoon in the North Pacific) is also affected by Coriolis force. The motive force of tropical cyclone movement is the pressure difference between the low pressure center and the surrounding atmosphere. The air in the surrounding atmosphere moves directionally to the center of low pressure driven by pressure difference, and is deflected by Coriolis force to form a rotating airflow, which rotates counterclockwise in the northern hemisphere and clockwise in the southern hemisphere. Due to the rotation, the low pressure center can be maintained for a long time.

Effect of 5 on molecular spectrum

Coriolis force will affect the vibrational rotation spectrum of molecules. The vibration of molecules can be regarded as the linear motion of particles, and the rotation of the whole molecule will affect the vibration, thus coupling the original independent vibration and rotation. In addition, due to the existence of Coriolis force, the original independent vibration modes will also exchange energy, which will affect the infrared spectrum and Raman spectrum behavior of molecules. During this period, people used the principle of Coriolis force to design some instruments for measurement and motion control.

1 mass flowmeter

The mass flowmeter allows the measured fluid to pass through a rotating or vibrating measuring tube. The flow of fluid in the tube is equivalent to linear motion, and the rotation or vibration of the measuring tube will produce an angular velocity. Because the rotation or vibration is driven by an external electromagnetic field and has a fixed frequency, the Coriolis force on the fluid in the pipe is only related to its mass and velocity, and the product of mass and velocity, that is, flow, is the mass flow to be measured. Therefore, by measuring the Coriolis force on the fluid in the tube, its mass can be measured.

The same principle is also applicable to the powder dosing scale, in which powder can be approximately regarded as fluid treatment.

gyro

The rotating gyroscope will reflect various forms of linear motion, and the motion can be measured and controlled by recording the Coriolis force on the gyroscope assembly.

* 2.7 Coriolis acceleration The two reference frames in this paragraph of Coriolis acceleration editor can rotate with each other. For example, when the high-speed centrifuge is started, the test tube reference system and the desktop reference system rotate relatively. The particles in the test tube move in a straight line along the test tube, but spiral relative to the desktop, so we also need to transform the rotating coordinate system.

Consider the disk S' rotating relative to the desktop S, as shown in Figure 2- 17. Let the rotational angular velocity ω be a constant vector, pointing to the positive direction perpendicular to the Z axis of the disk surface, with the rotational axis at the center O' of the disk surface and the origin o of the desktop coincident with it. Suppose that vector a is fixed on S'. Note that the velocity expression (2.2. 10) shows that the increment of a in dt time is

dA=A(t+ dt)- A(t)=(ω×A)dt

If the vector has an increment dA' relative to s' at the same time, the increment relative to s is

Da = (ω× a) dt+da So we have a general relationship:

Or write a symbolic equation:

Obviously, the transformation relation of speed can be obtained by substituting the position vector into the above formula:

The derivative with apostrophe in the formula only means that it is carried out in the S' system, and does not mean that there is any difference in time. This also applies to other vectors. For example, any vector can be replaced by two vectors starting from the origin. The above practice can be completely extended to three-dimensional situations. The symbolic equation (2.7.2) is linear (satisfying the distribution law). For the velocity vector, we have

As can be seen from the observers in the S system, the acceleration consists of three parts. The first item is in the S' system.

Acceleration. When the particle is stationary in the S' system, the meaning of the third term can be clearly seen:

ω×(ω×r)=-(ω ω)ρ (2.7.5)

That is, centripetal acceleration. The second term is called Coriolis acceleration, which has a non-zero value only when the particle moves in the S' system. Is the expression *(2.7.4) consistent with the expression of acceleration in plane polar coordinates (1.5)? If the angular velocity is not a constant vector, are equations (2.7.3) and (2.7.4) correct? If it is not correct, how should it be revised?

Let's discuss the influence of the earth's rotation. The rotating earth is considered as an S' system, and a "non-rotating" earth (translation coordinate system) is an S system. In the earth reference system, the acceleration of gravity of particles is

g = G0-2ω×v′-ω×(ω×r)(2 . 7 . 6)

we know

G0 ≈ 9.8m/s2

ω= 7.292× 10-5 radians/second

In contrast, the inertial centrifugal term is much smaller,

|ω×(ω×r)|≤ω2R≈3.39× 10-2m/S2 < < G0

Thus, if the effective acceleration of gravity is incorporated, the formula (2.7.6) can be written as follows.

mg = mg eff-2mω×v′(2 . 7 . 7)

The last term is the Coriolis force on a moving object. It should be noted that this term is completely transformed from the coordinate system, or it is produced because the observer's perspective in the rotating coordinate system is different from that in the translating coordinate system. Generally, we can say that Coriolis force is a kinematic effect. * Is Coriolis force related to latitude? Is there a difference between the southern hemisphere and the northern hemisphere?

According to formula (2.7.7), we can judge the deviation of falling body. Roughly speaking, the speed (zero order approximation) of a falling body is in the -r direction. For the northern hemisphere, we can judge that the speed will be biased to the east, that is, -2mω×v' ~ωk×er =ωEJ. The so-called falling body is eastward. If it is from (2.7)

* Discussion: Will the thrown object fall at the throwing point?

The movement of the earth's surface is also influenced by Coriolis force. As can be seen from Figure 2- 18, rotation causes the movement to deviate from the forward right hand direction. We can decompose the speed to obtain quantitative results:

-2ω×(vθeθ+vjej)= 2ω(vθeθ×k+vjej×k)

=2ω(-vθcosθej+vjeρ)

=2ωcosθ(-vθej+vjeθ)

+2ωvjsinθer

Because of the existence of the g term, the radial term in the formula can be ignored, and the first two terms accurately indicate that the acceleration points to the right hand side of the motion direction.

A typical example of Coriolis force is cyclone in the atmosphere. In the weather forecast program, you may have seen the counterclockwise cyclone in the satellite image. In the southern hemisphere, this cyclone is clockwise. Foucault's pendulum (18 19- 1868) is an excellent example to show the earth's rotation. 36866.88686868686

Coriolis force is also manifested in microscopic phenomena. For example, it makes molecules rotate.