# Earth’s rotational motion: characteristics and consequences

The Earth’s rotational movement is what our planet performs around the Earth’s axis in the west-east direction and has a duration of approximately one day, specifically 23 hours, 56 minutes and 3.5 seconds.

This movement, along with the translation around the sun, is the most important thing the Earth has. In particular, the rotation movement is very influential in everyday life, as it generates days and nights.

Therefore, each time interval has a certain amount of sunlight, which is commonly called day and no sunlight or night . The Earth’s rotation also involves changes in temperature, as day is a period of warming, while night is a period of cooling.

These circumstances mark a milestone in all living beings that populate the planet, giving rise to a multitude of adaptations in terms of lifestyle habits. According to her, societies established periods of activity and rest according to their customs and influenced by the environment.

Obviously, the areas of light and dark change as movement occurs. When dividing 360º that it has a circumference, between the 24 hours in which a day is rounded, it appears that in 1 hour the Earth turned 15º in a west-east direction.

So if we move west 15° is an hour earlier, the opposite happens if you travel east.

The Earth’s rotation speed on its own axis has been estimated to be 1600 km/h at the equator, with the consequent decrease as it approaches the poles, until it ends up canceling out just above the rotation axis.

## Characteristics and causes

The reason the Earth rotates on its axis is found in the origins of the solar system. Possibly the Sun passed long after gravity made it possible for it to be born out of the amorphous matter that inhabits space. When formed, the Sun acquired the rotation provided by the primitive cloud of matter.

Some of the matter that gave rise to the star was compressed around the Sun to create the planets, which also had their share of the original cloud’s angular momentum. In this way, all planets (including Earth) have their own rotational motion in a 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, because of the impact, changed its axis and sense of rotation. On Venus, the existence of gas tides could explain that the direction of rotation slowly reversed over time.

### angular momentum

Angular momentum is, in rotation, what is the amount of linear motion for the translation. For a body that rotates around a fixed axis like the Earth, its magnitude is given by:

L = Iω

In this equation L is the angular momentum (kg.m 2 / s), I is the moment of inertia (kg.m 2 ) and w is the angular velocity (radians / s).

Angular momentum is preserved 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 are considered as an isolated system, in which no force caused an external torque.

#### Exercise solved

Assuming the Earth is a perfect sphere and behaves like a rigid body and using the given 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 = I sphere = (2/5) MR 2 ; Earth Mass M = 5,972 · 10 24 Kg, Earth radius R = 6371 Km; average distance between the Earth and the Sun R m = 149.6 x 10 6 Km.

##### Solution

a) First, you need to consider the Earth’s moment of inertia as a sphere of radius R and mass M.

I = (2/5) ´ 5,972 · 10 24 Kg ′ ( 6371 ´ 10 3 Km) 2 = 9.7 ´ 10 37 kg.m 2

Angular velocity is calculated as follows:

ω = 2π / T

Where T is the movement period, which in this case is 24 hours = 86400 s, therefore:

ω = 2π / T = 2π / 86400 s = 0.00007272 s -1

The angular momentum of rotation about its own axis is:

L = 9.7 ´ 10 37 kg.m 2 ´ 0.00007272 s -1 = 7.05 ´ 10 33 kg.m 2 / s

b) With regard to the translational movement around the Sun, the Earth can be considered a point object, whose moment of inertia is I = MR m

I = MR m = 5.972 x 10 24 kilograms ‘ (149.6 ‘ from October 6 × 1.000 m) 2 = 1. 33 ’10 47 kg.m two

In one year, there are 365 × 24 × 86400 s = 3.1536 × 10 7 s, the Earth’s orbital angular velocity is:

ω = 2π / T = 2π /3.1536 x 10 7 s = 1.99 x 10 -7 s -1

With these values, the Earth’s orbital angular momentum is:

L = 1. 33 ´10 47 kg.m 2 × 1.99 × 10 -7 s -1 = 2.65 × 10 40 kg.m 2 / s

## Consequences of the rotation movement

As mentioned above, the succession of days and nights, with their respective changes in the hours and temperature of the day, are the most important consequences of the Earth’s rotational movement on its own axis. However, its influence extends a little beyond this decisive fact:

– The Earth’s rotation is closely related to the shape of the planet. The Earth is not a perfect sphere like a billiard ball. As it rotates, forces develop that deform it, causing the equator to bulge and, consequently, flattening at the poles.

– Earth deformation generates small fluctuations in the value of gravity acceleration g at different locations. For example, the value of g is greater at the poles than at the equator.

– The rotational movement greatly influences the distribution of sea currents and greatly affects the winds, because the air and water masses deviate from the trajectory in a clockwise direction (northern hemisphere) and in the opposite direction (southern hemisphere).

– Time zones were created to regulate the passage of time in each location as different areas of the Earth are lit by the sun or darkened.

### Coriolis Effect

The Coriolis effect is a consequence of the Earth’s rotation. As acceleration exists at all rotations, the Earth is not considered an inertial frame, which is necessary to apply Newton’s laws.

In this case, so-called pseudo-forces appear, forces whose origin is not physical, such as the centrifugal force experienced by passengers in a car when it bends and they feel that they are deflected to the side.

To visualize its effects, consider the following example: There are two people A and B on a counterclockwise rotating platform, both at rest relative to it. Person A throws a ball at person B, but when the ball hits the place where B was, he 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 outside the center. It’s about the Coriolis force, whose effect is to deflect the ball sideways. It turns out that A and B have different upward speeds, because they are at different distances from the axis of rotation. The speed of B is greater and is given by:

Um = ω A ; v B = ω B

### Coriolis acceleration calculation

Coriolis acceleration has significant effects on the movement of air masses and therefore affects the climate. Therefore, it is important to consider the study of how air currents and ocean currents move.

People can also experiment when they try to ride on a platform that is spinning, 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 observed by the ball from the original position of person B is:

s = B – s A = vt = (v B – v A ) t = (ω B – ω A ) t = ω (R B – R A ) t

But B – R A = vt, so:

s = ω . (vt). t = ω vt 2

It is a movement with an initial velocity of 0 and constant acceleration:

s = ½ to Coriolis t 2

for Coriolis = 2ω .v