Basic earth movements. Rotation of the earth around its axis Effect of daily rotation of the earth on body weight

The Earth, rotating from west to east (when viewed from the North Pole), makes a complete revolution around its axis in 24 hours. The angular speed of rotation of all points of the Earth is the same (15 ° per hour). The linear speed of rotation of points depends on the distance that they must travel during the period of the Earth's daily rotation. Only the exit points of the imaginary axis - the points of the geographical poles (North and South) - remain stationary on the surface of the Earth. With the highest speed (464 m / s) points rotate on the equator line, on the line of the great circle formed by the intersection of the Earth by a plane perpendicular to the axis of rotation. If you mentally cross the Earth by a number of planes parallel to the equator, lines will appear on the earth's surface with a west-east direction, called parallels... The length of the parallels decreases from the equator to the poles, and the linear speed of rotation of the parallels decreases accordingly. The linear speed of rotation of all points on one parallel is the same.
When the Earth intersects with planes passing through the Earth's axis of rotation, lines appear on its surface with a north-south direction, meridians (meridianus, lat. - noon). The linear speed of rotation of all points on one meridian is not the same: it decreases from the equator to the poles.
The experiment with a swinging pendulum (Foucault's experiment) serves as convincing proof of the rotation of the Earth around its axis.
According to the laws of mechanics, any swinging body tends to keep the swing plane. A freely suspended swinging pendulum does not change the swing plane, and at the same time, if a circle with divisions is placed with a pendulum on the surface of the Earth, it turns out that in relation to this circle (i.e., relative to the Earth's surface) the position of the swing plane of the pendulum changes. This can only happen due to the fact that the surface of the Earth rotates under the pendulum. At the pole, the apparent rotation of the swinging plane of the pendulum will be 15 ° per hour; at the equator, the position of the swinging plane of the pendulum does not change, since it all the time coincides with the meridian; at intermediate latitudes, the apparent rotation of the rocking plane is 15 ° sin φ per hour (φ is the latitude of the observation site).
Deflecting action of the Earth's rotation (Coriolis force) is one of the most important consequences of the Earth's rotation. We usually orient the direction of motion of bodies in relation to the sides of the horizon (north, south, east, west), that is, in relation to the lines of meridians and parallels, forgetting that these lines, due to the rotation of the Earth, continuously change their orientation in world space ... A body in motion, according to the law of inertia, seeks to maintain the direction and speed of its movement relative to world space. For example, let a rocket be launched from point A (in the northern hemisphere) towards the North Pole (Fig. 13). At the moment of launch, the direction of its movement (AB) coincides with the direction of the meridian. Ho already at the next moment, point A, as a result of the Earth's rotation, will move to the right, to point B. The direction of the meridian in space will change, the meridian will deviate to the left. The rocket, on the contrary, will retain the direction of movement, while it seems to an observer watching its movement that it has deviated to the right under the influence of some force. It is easy to understand that this force is fictitious, for the rocket only seems to deviate due to a change in the direction of the meridian, along which the observer orients the direction of its movement. If the body moves in the northern hemisphere from north to south, the meridian changes its direction, moving to the left, and the observer sees the moving body deviating, as well as when moving from south to north, to the right.

The deviation will be greatest at the poles, since there the meridian changes its direction in world space by 360 ° per day. The deviation from the poles and the equator decreases, and at the equator, where the meridians are parallel to each other and their direction in space does not change, the deviation is 0.
In the southern hemisphere, the deflecting action of the Earth's rotation is manifested in the deflection of moving bodies to the left.
Bodies moving in any direction deviate from the direction of movement to the right in the northern hemisphere and to the left in the southern hemisphere.
The deflecting force of the Earth's rotation (Coriolis force), acting on a unit of mass (1 g) moving at a speed of V m / s, is expressed by the formula F \u003d 2ω * v * sin φ, where φ is the angular speed of the Earth's rotation, φ is latitude. The Coriolis force does not depend on the direction of motion of the body and does not affect its speed.
The deflecting effect of the Earth's rotation has a constant effect on the direction of motion of all bodies on the Earth, in particular, it significantly affects the direction of air and sea currents.
Change of day and night on Earth. The sun's rays always illuminate only half of the Earth facing the Sun. The rotation of the Earth around its axis causes the rapid movement of solar illumination across the earth's surface from east to west, i.e., the change of day and night.

If the earth's axis were perpendicular to the plane of the orbit, the light-dividing plane (the plane dividing the earth into illuminated and unlit halves) would divide all latitudes into two equal parts and at all latitudes, day and night would always be equal. When the axis is tilted to the plane of the earth's orbit, day and night can be equal at all latitudes only at the moment when the earth's axis lies in the dividing plane and when the dividing line (the line formed by the intersection of the earth's surface with the dividing plane) passes through the geographic poles. When the earth's axis is tilted with its northern end to the Sun (Fig. 14, a), the dividing plane, crossing the earth's axis at the center of the Earth, divides the Earth into two halves so that most of the northern hemisphere is illuminated, and the smaller part falls into the shadow, and vice versa most of the southern hemisphere is in shadow. If the axis of the Earth is tilted toward the Sun by its southern end (Fig. 14, b), the southern hemisphere is illuminated more than the northern one. Since the dividing line in both cases does not pass through the geographic poles and divides all latitudes, except 0 °, into two unequal parts - illuminated and unlit, day and night at all latitudes, except for the equator, are not equal. In the hemisphere that is tilted towards the Sun, the day is longer than the night; in the opposite hemisphere, on the contrary, the night is longer than the day. At those latitudes that are not crossed by the dividing line and for some time are completely on the illuminated or unlit side of the Earth, during the corresponding period (up to six months at the poles), the change of day and night does not occur. If the change of day and night is determined by the rotation of the Earth about the axis, and their inequality is determined by the inclination of the axis to the Earth's orbit, then the constant change in the duration of day and night at all latitudes, except for the equator, is the result of the constant position of the Earth's axis in space when the Earth revolves around the Sun.

Our planet is in constant motion, it revolves around the sun and its own axis. The Earth's axis is an imaginary line drawn from the North to the South Pole (they remain motionless during rotation) at an angle of 66 0 33 ꞌ with respect to the plane of the Earth. People cannot notice the moment of rotation, because all objects move in parallel, their speed is the same. It would look exactly the same as if we were sailing on a ship and did not notice the movement of objects and objects on it.

A full rotation around the axis is completed during one sidereal day, consisting of 23 hours 56 minutes and 4 seconds. During this interval, one or the other side of the planet turns to the Sun, receiving from it a different amount of heat and light. In addition, the rotation of the Earth around the axis affects its shape (the flattened poles are the result of the rotation of the planet around the axis) and the deflection when bodies move in the horizontal plane (rivers, currents and winds of the Southern Hemisphere deflect to the left, the Northern - to the right).

Linear and angular rotation speed

(Rotating the Earth)

The linear speed of the Earth's rotation around the axis is 465 m / s or 1674 km / h in the equator zone, as the distance from it gradually slows down, at the North and South poles it is equal to zero. For example, for the citizens of the equatorial city of Quito (the capital of Ecuador in South America), the rotation speed is just 465 m / s, and for Muscovites living on the 55th parallel north of the equator, it is 260 m / s (almost half as much) ...

Each year, the speed of rotation around the axis decreases by 4 milliseconds, which is associated with the influence of the Moon on the strength of sea and ocean ebb and flow. The Moon's gravity "pulls" the water in the direction opposite to the Earth's axial rotation, creating a slight frictional force that slows down the rotation speed by 4 milliseconds. The speed of angular rotation remains the same everywhere, its value is 15 degrees per hour.

Why does the day turn to night

(The change of night and day)

The time of a complete revolution of the Earth around the axis is one sidereal day (23 hours 56 minutes 4 seconds), during this time interval the sunlit side is at first "in the power" of the day, the shadow side - of the night, and then vice versa.

If the Earth rotated differently and one side of it was constantly turned towards the Sun, then there would be a high temperature (up to 100 degrees Celsius) and all the water would evaporate, on the other side - on the contrary, frosts raged and the water was under a thick layer of ice. Both the first and second conditions would be unacceptable for the development of life and the existence of the human species.

Why the seasons change

(Changing seasons on Earth)

Due to the fact that the axis is inclined with respect to the earth's surface at a certain angle, its sections receive at different times a different amount of heat and light, which causes the change of seasons. According to the astronomical parameters necessary to determine the time of year, some points in time are taken as reference points: for summer and winter, these are the Solstice Days (June 21 and December 22), for spring and autumn - the Equinox (March 20 and September 23). From September to March, the Northern Hemisphere is turned towards the Sun for less time and, accordingly, receives less heat and light, hello winter, winter, the Southern Hemisphere at this time receives a lot of warmth and light, long live summer! 6 months pass and the Earth moves to the opposite point of its orbit and already the Northern Hemisphere receives more heat and light, the days become longer, the Sun rises higher - summer is coming.

If the Earth were located in relation to the Sun exclusively in a vertical position, then the seasons would not exist at all, because all points on the half illuminated by the Sun would receive the same and uniform amount of heat and light.

The angular velocity of the Earth's rotation around the Sun (2π radians per year) is so small that the forces of inertia associated with it do not play a significant role in the processes taking place on the Earth. At the same time, the angular velocity of the Earth's daily rotation is approximately 365 times the angular velocity of its annual rotation. Therefore, when drawing up the equation of motion of a body in a frame of reference associated with the Earth, it is necessary to take into account not only Newtonian forces ( F), but also all inertial forces (centrifugal and Coriolis). At the same time, with rough quantitative estimates of the characteristics of some phenomena, it is often possible to neglect the inertial forces caused by the Earth's daily rotation, and the coordinate system associated with the Earth can be considered approximately inertial.

Thus, in accordance with the above reasoning, the Coriolis force manifests itself when moving along the surface of the globe due to the daily rotation of the Earth.

In the frame of reference connected with the Earth, the rotation of the swinging plane of the pendulum is explained by the action of the Coriolis force. At the pole, the speed of the pendulum ′ with a large length of its suspension can be considered perpendicular to the vector of the angular velocity of the Earth's rotation ω. Coriolis force according to the K2 formula, Fm′ \u003d Ω is perpendicular to the swinging plane of the pendulum and, according to the thumb rule, is directed to the right with respect to the relative speed of the pendulum. Since the Coriolis force is not balanced by any other force, as a result of its action, the swing plane of the pendulum turns. The trajectory of the pendulum will look like a rosette (Fig. 5.17). If the pendulum is installed at a certain latitude ϕ, then in this case its swing plane will rotate in a day by an angle 2sinπϕ. Thus, the experiment with the Foucault pendulum experimentally confirms that the frame of reference associated with the Earth is a non-inertial frame of reference.

The Coriolis force, which acts on a body moving at a relative speed ′ along the meridian, is directed relative to this speed to the right in the northern hemisphere and to the left in the southern (Fig.5.18, and). If the body moves in the equatorial plane from west to east, then the Coriolis force is directed vertically upward, when the body moves from east to west, it is directed vertically downward (Fig.5.18, b). The Coriolis force is zero if the body is moving at the equator in the meridian plane, because the vectors ω and ′ are parallel. An example of the influence of Coriolis forces on the movement of bodies near the surface of the globe is also the deviation of freely falling bodies to the east (Fig.5.18, at).

Coriolis forces play an important role in meteorological phenomena. So, the deflecting influence of the Coriolis force makes the powerful oceanic current of the Gulf Stream, leaving the Gulf of Mexico through the Florida

6. Mechanical system (MS). Classification of forces acting on the MS: external and internal forces, set (active) and link reactions. Properties of internal forces.

The globe makes a complex motion: it rotates about its axis, moves in an orbit around the Sun. It is quite clear that the Earth is not an inertial frame of reference. Nevertheless, we successfully use Newton's law in terrestrial conditions. However, in a number of cases, the non-inertial nature of the Earth affects quite sharply. We must study these cases.

Influence of the Earth's rotation on its shape. Body weight.

If we do not take into account the rotation of the Earth, then a body lying on its surface should be considered as oscillating.

The sum of the forces acting on this body would then be equal to zero. In fact, any point on the surface of the globe lying at a geographic latitude moves about the axis of the globe, i.e., in a circle with the radius of the Earth's radius, considered in the first approximation as a ball), with an angular velocity Consequently, the sum of the forces acting on such a point other than zero is equal to the product of mass and acceleration and is directed along

It is obvious that the presence of such a resultant force (Fig. 13)

is possible only if the reaction of the earth's surface and the force of gravity are directed at an angle to each other. Then the body will press on the surface of the Earth (according to Newton's third law) with force. If the earth were at rest, then this force would be equal to the force of gravity and would coincide with it in direction.

Let's decompose the force into two: directed along the radius and tangentially. The presence of the Earth's rotation leads, as we can see from the drawing, to two facts. First, the weight (the pressure of the body on the Earth) has become less than the force of gravity. Since this decrease is equal. Secondly, a force arises that tends to flatten the Earth, to move matter to the equator; this force Such flattening did take place; The earth has not a ball shape, but a shape close to an ellipsoid of revolution. As a result of this action, the equatorial radius of the Earth becomes approximately a fraction greater than the polar radius.

The flattening forces made the masses of the globe move until it took an equilibrium shape. When the displacement process ended, the flattening forces apparently ceased to operate. Consequently, the pressure forces acting on the surface of the globe are directed along the normal to the surface.

Let us now return to the magnitude of the body's pressure on the ground, that is, to the physical magnitude that is commonly called weight. The calculation made for the ball (the force of gravity minus, of course, is not valid for the true figure of the Earth. However, for approximate calculations, this result can be used.

At the pole, the weight of the body is equal to the force of gravity. Let us denote by the force of gravity of the body at the pole. Then the pressure of the body on the earth's surface at any point of the globe, in other words, the weight of the body, will be equal, as mentioned above, the difference between the force of gravity and the force, i.e.

The earth makes 11 different movements, of which the following are of great geographic significance:

Daily rotation around the axis,

Annual revolution around the sun,

Movement around the common center of gravity of the Earth-Moon system.

As you know, the Earth rotates around its axis from west to east, turning in I second by 24.6Q.gQ \u003d wy part of a full revolution. SS

The daily rotation of the Earth around its axis has a noticeable effect on any body freely moving along the surface of the earth, and, in particular, on the movement of air.

Let's imagine the horizon plane at the North Pole (Fig. 32). With the Earth's daily rotation, this plane will obviously rotate around the pole point P in the direction shown by the arrow.

Let us assume that the air particle a, the motion of which is being considered, at a certain moment of time is at point b on the line of the meridian RA. Let the direction of motion of this particle, marked by an arrow, make a certain angle a with the direction of the meridian PA.

Figure: 33. Deflecting action of the Earth's rotation in the northern and southern hemispheres.

Consider the motion of a particle a relative to such a rotating horizon plane. Obviously, after some time the RA meridian will take the position of RAg. But a moving particle by inertia will tend to maintain the same direction

Figure: 32. Deflecting action of the Earth's rotation at the pole.

which she had at point b. Thus, the direction of motion of the particle at the point bx
will be parallel to its movement at point b, which is indicated by the arrow. But this direction of movement is with the direction of the meridian RA1
angle p, slightly larger than angle a.

The movement will occur as if some force deflects the air particle to the right of the direction of its initial movement.

We examined the motion of a particle near the pole. The same phenomenon will be observed, but only to a lesser extent, and at other latitudes of the northern hemisphere. In this case, the deviation will be the smaller, the smaller the latitude of the place. There is no such deviation at the equator.

In the southern hemisphere, the deviation occurs to the left of the original direction of travel.

In fig. 33 shows diagrams illustrating the deviation of p in the northern and southern hemispheres during the initial movement of the

air particles along the meridian. The figure shows the cases of motion of a particle from pole to equator and from equator to pole - Here: AB and CD are the initial directions of motion of some air particles in the northern hemisphere, coinciding with the direction of the meridian; AHVX and C1D1 are the subsequent directions of motion of the corresponding particles, after points A and C, due to the rotation of the Earth, took position L, and Cѵ

For the southern hemisphere, similar starting positions are represented by arrows A'B 'and C'D', followed by arrows AB and CD.

As you can see, in these cases in the northern hemisphere there is a deviation to the right from the initial direction of movement, and in the southern hemisphere - to the left.

Here we consider the cases of such movement when the initial direction of movement coincided with the direction of the meridian. In mechanics, it is proved that deflection is observed in any direction of motion and the deflecting force of the Earth's rotation is always directed perpendicular to the direction of motion. In the northern hemisphere, it is ‘directed to the right, at right angles to the direction of travel, and in the southern hemisphere to the left.

In reality, there is no deflecting force, and the deviation of the particle from the initial direction of motion is due only to the daily rotation of the Earth.

The influence of this deviation is manifested not only in the deviation of air movement, but also in a number of other phenomena. An example is that the right bank is steeper than the left in most of the large rivers of the northern hemisphere. This is due to the fact that the water, in its course, deviates all the time to the right and (continuously undermines the right bank.

A deviation to the right in the northern hemisphere can be observed in the distribution of warm and cold ocean currents. Thus, the warm Gulfstrom current, starting off the coast of the Gulf of Mexico, deviates to the right when moving northward and reaches the coast of Scandinavia.

Thus, any freely moving body moving in any direction, under the influence of the Earth's rotation, deviates in the northern hemisphere to the right, and in the southern hemisphere to the left.