The rotational motion of the earth is the one that our planet runs around the Earth's axis in a west-east direction and lasts approximately one day, specifically 23 hours, 56 minutes and 3.5 seconds.
This movement, along with the translation around the sun, are the most important that the Earth has. In particular, the rotational movement is very influential in the day-to-day life of living beings, since it gives rise to days and nights.
Therefore, each time interval has a certain amount of solar illumination, which is what is commonly called day, and absence of sunlight or night. The rotation of the Earth also carries changes in temperature, since the day is a period of warming, while the night is a cooling period..
These circumstances mark a milestone in all living beings that populate the planet, giving rise to a multitude of adaptations in terms of life habits. According to it, the companies have established the periods of activity and rest according to their customs and influenced by the environment..
Obviously, the light and dark zones change as the movement takes place. When dividing 360º that has a circumference, between the 24 hours to which a day is rounded, it turns out that in 1 hour the earth has rotated 15º in a west-east direction.
Therefore, if we move to the west 15º it is one hour earlier, the opposite happening if we travel to the east.
The speed of rotation of the Earth on its own axis has been estimated at 1600 km / h at the equator, with the consequent decrease as it approaches the poles, until it cancels out just on the axis of rotation..
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The reason that the Earth rotates around its axis lies in the origins of the solar system. Possibly the Sun spent a long time only after gravity made possible its birth from the amorphous matter that populates space. As the Sun formed, it acquired the rotation provided by the primitive cloud of matter..
Some of the matter that gave rise to the star was compacted around the Sun to create the planets, which also had their share of the angular momentum of the original cloud. In this way, all planets (including Earth) have their own rotation movement in the west-east direction, except Venus and Uranus, which rotate in the opposite direction..
Some believe that Uranus collided with another planet of similar density and, due to the impact, changed its axis and direction of rotation. On Venus, the existence of gaseous tides could explain why the direction of rotation slowly reversed over time..
Angular momentum is, in rotation, what linear momentum is to translation. For a body rotating around a fixed axis like the Earth, its magnitude is given by:
L = Iω
In this equation L is the angular momentum (kg.mtwo/ s), I is the moment of inertia (kg.mtwo) Y w is the angular velocity (radians / s).
The angular momentum is conserved as long as there is no net torque acting on the system. In the case of the formation of the solar system, the Sun and the matter that gave rise to the planets is considered as an isolated system, on which no force caused an external torque.
Assuming that the Earth is a perfect sphere and behaves like a rigid body and using the supplied data, its angular momentum of rotation must be found: a) around its own axis and b) in its translational motion around the Sun.
Data: moment of inertia of a sphere = Isphere = (2/5) MRtwo; land mass M = 5.9721024 Kg, radius of the Earth R = 6371 Km; mean distance between the Earth and the Sun Rm = 149.6 x 106 Km.
a) First it is necessary to have the moment of inertia of the Earth considered as a sphere of radius R and mass M.
I = (2/5) ' 5,972 1024 Kg '(6371'103 Km)two = 9.7 '1037 kg.mtwo
The angular velocity is calculated like this:
ω = 2π/ T
Where T is the period of the movement, which in this case is 24 hours = 86400 s, therefore:
ω = 2π/ T = 2π/ 86400 s = 0.00007272 s-1
The angular momentum of the rotation around its own axis is:
L = 9.7 '1037 kg.mtwo' 0.00007272 s-1 = 7.05'1033 kg.mtwo/ s
b) Regarding the translational motion around the Sun, the Earth can be considered a point object, whose moment of inertia is I = M.Rtwom
I = M.Rtwom= 5,972 1024 Kg'(149.6 ' 106 × 1000 m)two = 1. 33'1047kg.mtwo
In a year there are 365 ×24 × 86400 s = 3.1536 × 107 s, the orbital angular velocity of the Earth is:
ω = 2π/ T = 2π/3.1536 × 107 s = 1.99 ×10-7 s-1
With these values the orbital angular momentum of the Earth is:
L = 1. 33'1047kg.mtwo × 1 .99 × 10-7 s-1 = 2.65 × 1040 kg.mtwo/ s
As mentioned above, the succession of days and nights, with their respective changes in the hours of light and temperature, are the most important consequence of the rotational movement of the Earth on its own axis. However, its influence extends a little beyond this decisive fact:
- Earth's rotation is closely related to the shape of the planet. Earth is not a perfect sphere like a billiard ball. As it rotates, forces develop that deform it, causing bulging at the equator and consequent flattening at the poles..
- The deformation of the Earth gives rise to small fluctuations in the value of the acceleration of gravity g in different places. For example, the value of g is greater at the poles than at the equator.
- Rotational motion greatly influences the distribution of ocean currents and greatly affects winds, due to the fact that air and water masses experience deviations from their trajectory both clockwise (northern hemisphere) and clockwise. opposite direction (southern hemisphere).
- The time zones, in order to regulate the passage of time in each place, as different areas of the Earth are illuminated by the sun or darkened.
The Coriolis effect is a consequence of the Earth's rotation. Since there is acceleration in all rotation, the Earth is not considered an inertial frame of reference, which is what is needed to apply Newton's laws.
In this case, the so-called pseudo-forces appear, forces whose origin is not physical, such as the centrifugal force experienced by the passengers of a car when it makes a curve and they feel that they are deflected to one side..
To visualize its effects, consider the following example: there are two people A and B on a platform in counterclockwise rotation, both at rest with respect to it. Person A throws a ball to person B, but when the ball reaches the place where B was, it has already moved and the ball is deflected a distance. s, passing behind B.
The centrifugal force is not responsible in this case, it already acts out of the center. This is the Coriolis force, the effect of which is to deflect the ball laterally. It happens that both A and B have different upward speeds, because they are at different distances from the axis of rotation. The speed of B is higher and they are given by:
vTO = ωRTO ; vB = ωRB
The Coriolis acceleration has significant effects on the movement of air masses, and therefore affects the climate. That is why it is important to take it into account to study how air currents and ocean currents move..
People can also experience it when they try to walk on a rotating platform, such as a moving carousel..
For the case shown in the previous figure, suppose that gravity is not taken into account and the movement is visualized from an inertial reference system, external to the platform. In this case, the movement looks like this:
The deviation s experienced by the ball from the original position of person B is:
s = sB - sTO = vt = (vB - vTO) t = (ωRB - ωRTO) t = = ω(RB - RTO) t
But RB - RTO = vt, then:
s = ω .(vt). t = ωvttwo
It is a movement with initial velocity 0 and constant acceleration:
s = ½ aCoriolis ttwo
toCoriolis = 2ω.v
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