A Foucault pendulum can be used to demonstrate that earth is rotating. Explain how this is possible. What differences would you notice if you used the pendulum at the North Pole, at Earth's equator, and at altitudes between two points?

Answer 1

You must mean latitudes, not altitudes.

A concise derivation of the equation for the rotation of the plane of oscillation of a Foucault pendulum is hard to find. I once spend a half day in the college library looking for one, reviewing musty leather-bound journals over 150 years old. I finally found one.

It is not hard to convince yourself that the plane of oscillation (referred to ground-fixed coordinates) rotates once every 24 hours at the north and south poles, as the earth rotates below the pendulum. At the equator, the plane remains the same.

At an intermediate latitude A, the plane of oscillation rotates with a period (24 h)/|sin A|. You can think of the ground below as undergoing a combination of translation and rotation. The angle of rotation is determined by "unfolding" a conical surface that is tangent to the Earth as it makes one full rotation below the pendulum.