# Linear speed of a point on Earth's surface as a function of its latitude The planet Earth has three motions: first, it moves through our galaxy, the Milky Way, along with the other objects in the Solar System. Then, it revolves around the Sun and last, it rotates about its axis.

When it comes to the rotation about its axis, the Earth takes approximately 24 hours to complete one rotation. This time is known as period (T) of rotation.

The period of rotation is defined as the time an object takes to complete a single revolution about its axis.

On the other hand, the angular speed (ω) of the rotating object is given by: where the period T has to be given in seconds.

Therefore, the angular speed of the Earth is: In the result above, radian (rad) is the SI unit for measuring angles.

Each and every point on the surface of the Earth undergoes circular motion at the same angular speed ω, because all of them take the same time to complete a revolution. However, not every point on the surface of the Earth moves at the same linear speed.

In a circular motion, the relationship between the linear (v) and the angular speed (ω) is: where R is the radius of the circle described by the point undergoing circular motion. In the figure above, the radius (R) of any point P on the surface of the Earth is shown in red. This radius is the distance from the point P to the Earth’s axis of rotation. As can be seen in the figure, this distance is different depending on the latitude λ of the point and is not the same as the radius of the Earth RT.

Latitude is defined as the angle formed by the perpendicular to the surface at any point on the surface of the Earth and the equatorial plane.

In order to find the linear speed of a point on the surface of the Earth, we must first find the radius R of point P as a function of its latitude.

We can find R with the aid of the trigonometric function sine using the triangle shown in the figure below.   And by substituting this expression into the definition of linear speed, we get: The latitude of both the North and South poles is 900, and therefore their linear speed is zero (they are at rest).

The latitude of any point on the Equator is zero, and therefore the linear speed will reach its maximum value, given by: The linear speed of any other point on the surface of the Earth will have a value between these two extreme cases, as seen in the figure below. The fact that the linear speed of the points on Earth’s surface depends on their latitude is responsible for the Coriolis effect.

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