# Foucault Pendulum

Posted on Feb 5, 2014

On the poles, the plane of the pendulum swing would make one rotation each day. On the equator, however, the plane will not rotate at all. This begs the question of why the plane rotates. Due to rotating reference frames and the Coriolis force, the pendulum rotates at a different rate at different latitudes. If your frame of reference were on the earth, then depending on where you stand, the earth will be moving  at different speeds.

Suppose we were standing on the North Pole. In our reference frame, the earth would rotate clockwise making hanging objects appear as though they were rotating counterclockwise. At the North Pole, you are on the axis of spin, and would therefore only see the affects of rotation. If you stand on the equator, keeping the axis of rotation at a constant angle, the earth does not rotate in your reference frame. As you move closer to the pole, the rotation in your reference frame becomes greater and greater. This allows for different amounts of rotation on different latitudes for the Foucault Pendulum. The amount of rotation per day for the pendulum can be found using the following formula. N=360*sin(x), where x is the latitude in degrees and N is the amount of rotation per day. Another way to think about the rotating frame of reference is to think of a child on a merry-go-round. If the child is spinning around and lets go of a ball, anybody watching would see the ball go in a straight line off the merry-go-round. But in the reference frame of the child, it appears that there is some force making the ball curve, as the child must turn his or her head in order to keep seeing the ball. So, just as the child on the merry-go-round thinks there is some force pulling on the ball after it left their hand, we think there is a force pulling things in directions since we are on a spinning ball. This is the Coriolis force that we mentioned...

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