If I make a pendulum that swings freely, but its ‘holder’ is stuck to the earth. Can the earth rotate underneath it?

Answer

Indeed, the earth is spinning under the pendulum. The effect depends on your position on Earth.

This can be used to show the rotation of the earth. You can find such Faucoult garlands in various museums around the world.

See for example:

http://www.flickr.com/photos/checco/3337258773/

http://www.cleonis.nl/physics/phys256/foucault_stereograph.php