# Rotation of the Earth and the pendulum

At first glance it may seem that the circumstance when people for a long time could not prove that they live on a rotating planet is trivial. But it turned out that proving **Earth rotation** around its own axis is not so easy. All because the rotation of other celestial bodies can be seen on the basis of direct observations. For example, the rotation of the Sun can be detected by the movement of sunspots, the rotation of the planet Mars - by the displacement of details visible on its surface. The rotation of the Earth, people could not observe from the side.

A clear and simple proof of the Earth's rotation was the swinging **pendulum** Foucault - a load suspended on a string. The driven, freely suspended pendulum will swing all the time in the same plane. But in order to reliably detect the rotation of the swinging plane of the pendulum due to the rotation of the Earth, it takes quite a long time.

This disadvantage is added Poshekhonov's pendulum, with which you can quickly find the rotation of the Earth. The action of this pendulum is based on the law of conservation of angular momentum. Imagine a vertically placed frame mounted on a stand and capable of rotating about a vertical axis. In the center of the frame on the horizontal axis, a freely rotating bar with weights at the ends is fixed. That's the whole device.

The moment of momentum is the product of the mass of a given body *m* by its linear velocity *V* and by a distance *R* from the axis of rotation. But the linear velocity is equal to the product *R* by the angular velocity *ω (V = R*ω)*. So *N = m*ω*R ^{2}*, where

*m*is a constant value.

Now let's assume that the radius *R* decreases, that is, the body approaches the axis of rotation. Since *m* is constant, so that the product *ω*R ^{2}* does not change,

*ω*, that is, as the rotating masses approach the axis of rotation, the angular velocity increases.

We will force the central rod of the pendulum to rotate about the horizontal axis. When the bar is horizontal, that is, the loads are far from the vertical axis, the pendulum rotates with the stand. But at the moment when the rod comes to the vertical position and the loads at its ends are on the axis of rotation of the stand, the angular speed of rotation of the frame relative to the vertical axis will increase. And the frame along with the bar should make a "jerk", overtaking the rotation of the stand. Thus, there will be a gradual rotation of the plane of rotation of the rod. It is easy to see that this principle allows one to judge the rotation of the stand, without even observing it directly. And this means that with the help of Poshekhonov's pendulum, one can also detect the diurnal rotation of the Earth.

The diurnal rotation of the Earth can be seen from outer space, studying the motion of its artificial satellites.

On an artificial satellite, moving along a near-earth orbit, in fact, only the force of gravity, which lies in the plane of this orbit. Due to this, the plane of the satellite's orbit for short periods of time does not change its position relative to the stars. If the globe did not rotate around its axis, then the satellite would pass over the same points of the earth's surface at each successive revolution. But due to the fact that the Earth rotates from west to east, the route of the satellite, that is, the projection of its movement on the surface of the Earth, is continuously shifting towards the west.