# Foucault’s Pendulum

In this article, Derek Williams explains the background to Foucault’s famous pendulum; an example of which can be seen at Preston’s Harris Museum. Two French stamps recognise Foucault’s achievements.

The pendulum is a weight suspended from a pivot so it can swing freely. The first to investigate this was Galileo and his investigation came to the following conclusions.

- Pendulums nearly return to their release height.
- Lighter pendulums come to rest faster.
- Period is independent of bob weight.
- Period is independent of amplitude.
- Square of the period varies directly with length.

The period of swing of a simple gravity pendulum depends on its length and the acceleration due to gravity. The maximum angle that the pendulum swings away from the vertical, theta _{0}, is called the amplitude. It is independent of the mass of the bob. If the amplitude is limited to small swings, then the period T of a simple pendulum which is the time taken for a complete cycle is: –

T= sqrt of L/g, given theta_{ 0 } is less than 1

where L is the length of the pendulum and g is the local acceleration due to gravity.

Galileo failed to produce a successful timepiece based on the pendulum; Christian Huygens of the Netherlands produced the first pendulum clock.

Jean Bernard Léon Foucault (1819 – 1868), a French physicist and mathematician first studied as a surgeon but discovered he could not stand the sight of blood so transferred to the study of physics where he became famous for his experiments with the pendulum.

His first problem was to design a support for a pendulum which allowed it to freely move in any direction without any resistance. When set in motion, Foucault noticed that the plane of swing gradually turned, demonstrating clearly for the first time that the Earth rotates. He was asked to demonstrate his findings at the Paris Observatory. Every scientist in Paris received an invitation to view the pendulum in the Paris Observatory on 3^{rd} February 1851. The demonstration was a complete success.

Foucault’s Law for the time taken for complete rotation of the pendulum is

T = 24/sin(q),

where T is the time in hours taken for the pendulum to return to its original position and q is the latitude at which the experiment is carried out. At the Poles, it takes 24 hours to return to its original position while at the equator, it does not rotate at all.

The angular speed, α (measured in clockwise degrees per sidereal day) is proportional to the sine of the latitude z.

So α = 360^{0 }sin z.

The two French stamps below recognise Foucault and his pendulum.

1958 – French Scientists. SG1373

1994 – Foucault Pendulum shown on stamp commemorating the bicentennial of the National Conservatory of Arts and Crafts. SG 3225

The **Harris Museum in Preston, Lancashire** has a Foucault Pendulum as do many other buildings around the world. The pendulum is set in motion each day. Preston has a latitude of 53^{0} 45’, which gives a rotation time of approximately 30 hours.