Understanding Foucault Pendulums

[Daboo]

Simple question - I'm having trouble conceptually understanding why the plane that a Foucault pendulum swings in does not rotate with the earth. I understand how the Earth turns under the pendulum, but isn't the pendulum rotating with the Earth when it's released?

 

[AlephZero]

As a simple case, consider the pendulum is at the north or south pole.

If you pull the pendulum away from the vertical, hold it steady relative to the earth, and then release it, you are right that in relative to the non-rotating reference frame, initially it has a "sideways" component of velocity equal to omega.x, where omega is the Earth's rotation speed and x is the displacment.

Because of that, it will oscillate by moving round a very thin ellipse, not back and forth in a straight line. Ignoring the finite length of the pendulum, the motion is just two simple harmonic oscillations 90 degrees out of phase, i.e. x = A cos pt and y = B sin pt where A is very much bigger than B.

But the axes of the ellipse won't rotate with time (relative to the non-rotating reference frame) because there are no forces to make them rotate.

So relative to the relative to the earth, the pendulum oscillates in almost a straight line, and that line rotates once per day.

Hope that helps.

 

[Daboo]

Thanks! I wasn't properly understanding the concept of a reference frame. This really cleared it up for me:

http://www.youtube.com/watch?v=_36MiCUS1ro&mode=related&search=

 

[Loren Booda]

What qualifications does the Foucault pendulum suspension need to have? Can such a pendulum ever move in a (very thin) "figure eight"? Neat video.