# How does a pendulum demonstrate that the earth rotates?

Apr 15, 2016

Foucault's Pendulum demonstrates that earth rotates.

#### Explanation:

Foucault's Pendulum Observe in this picture that the rotation of the plane of swing of the pendulum, due to earth's rotation, causes knocking down of pins by bob at different positions as time passes.

A Foucault's pendulum, which has a huge metal bob is suspended with the help of a long metal wire from the roof of a suitable building (in the original experiment 28 kg brass-coated lead bob, a 67 metre long wire and dome of the Panthéon, Paris were used).

The plane of the pendulum's swing rotates clockwise, making a full circle in a time period depending on the latitude of the place where the pendulum is placed. Latitudes north of the equator are defined as positive and south of equator as negative. Therefore the rotation is anticlockwise in the southern hemisphere. .

From this figure it can be seen that effect of rotation of earth's rotation is maximum at the poles and no-effect at the equator.

Force equation for the bob at any instance of time $t$ is given by, (the derivatives of the radius vector are with respect to time)

$\text{Total Force"="Force of gravity"+"Tension in the metal wire"+"Coriolis force due to earth's rotation}$

$m \vec{\ddot{r}} ' = m \vec{g} + \vec{T} - 2 m \left(\vec{\omega} \times \vec{\dot{r}} '\right)$