# Foucault's Pendulum Physical Experiment

Updated on July 24, 2019

Started Aerospace Engineering at University Carlos III de Madrid (Spain). Currently studying at Purdue University (IN).

Earth's rotation was a matter of study that took origin with the Greeks in the V a.C, and many proofs of this were given, taking as main example the existence of day and night. However, it was not until the XIX century that an explanation based on an analysis from the Earth, and not on the sky analysis, was given by the distinguished physicist Leon Foucault.

## Pendulum Fundamentals

Firstly, we must start with a brief explanation of the functioning of a pendulum. A basic pendulum motion is based on the following principle: when the mass is displaced from the equilibrium position, there will appear a restoring force due to gravity in order to return it back, but due to the mass of the pendulum, there will be an oscillatory movement back and forth from that equilibrium position. Assuming that the pendulum will not lose energy due to friction, this movement would be repeated forever, and each of the repetitions would be called a period. For a broad explanation of this concept, I strongly recommend the Lectures of MIT professor Walter Lewin, as these concepts are explained in a clearly way to everyone.

## Inertial forces

Now, to understand Earth's rotation from this, we need to take into account the concept of relative movement. When we have a system of bodies subjected to different movements(with their respective forces and accelerations), we can use one of the bodies as a system of reference and study the movement of the other with respect to the first one(in fact, we are always doing this in mechanical physics problems, although we take several simplifications). However, when the body in which we attach the system of reference is a rotating body, two inertial forces appear: Coriolis force and centrifugal force. Notice that these forces are called "fictitious", and are used only to allow the application of Newton's laws to a rotating system. They are correction factors that do not exist in a non-accelerating or inertial reference frame.

## Earth's rotation problem

This concept application can be clearly seen in our case. Our system will be composed by a main body(where we attach our system of reference): the Earth, and a secondary body in relative movement: our pendulum(Foucault's pendulum). When applying a theoretical analysis, we discover that Foucault's pendulum will have an extra displacement due to Coriolis force, that will cause a modification of its path. It must be noted that the position of the pendulum in Earth is relevant, because as we approach to the equator, Coriolis force will reduce until vanishing, and in them, our pendulum will act as a simple pendulum. In the North and South poles, however, Coriolis force will be maximum, causing the greater displacement.

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