Understanding the Foucault Pendulum

Virtual Foucault Pendulum

This simulation shows two views of the motion of a Foucault Pendulum. The left view shows the 3D motion of the pendulum bob (gold sphere) suspended by a wire (black line) as it oscillates above a horizontal sand pit surrounded by a silver railing. A magenta arrow points North, while a transparent gray plane shows the pendulum's current plane of oscillation. The right view shows the same scene from above, with a blue curve tracing the motion of the bob.

Controls allow you to play/pause the simulation, advance the simulation by one time step, initialize the simulation using current settings, or reset the simulation to the default settings. Drop-down menus let you select the Earth's rotational speed, the length of the pendulum (selected from actual Foucault Pendulum lengths), and the location of the pendulum on Earth (with latitudes shown in parentheses). Displays show the elapsed time and the precession period, in hours. You can click and drag to rotate the 3D view on the left.

Explore!

Precession at the Poles

• Set the location to the North Pole, but keep the pendulum length at 16 m and the Earth's rotational speed on Normal. (Note: the direction of the north arrow is arbitrary at this location since from the North Pole every direction is southward.) Play the simulation. Does the pendulum's plane of oscillation precess noticeably in a short time? What is the period of the pendulum's precession? How does it compare to the length of a sidereal day (23.93 hours)?
• Set Earth's Rotation Speed to 100x. The simulation will now show the motion of the pendulum if the Earth rotated 100 times per sidereal day. Play the simulation and let it run for a little while. Can you see the precession? Does the plane of oscillation precess clockwise or counterclockwise? What is the period of the precession? How does this period compare to the period when Earth rotates normally?
• Now set the Earth's Rotation Speed to 1000x. Play th simulation and compare the behavior to the results seen previously.
• Switch the location to the South Pole and repeat that steps above. What is the difference in the precession betweeen the North and South Poles?

Precession at Other Locations

• Use the location selector to move to other locations on Earth, excluding the poles and the equator. You will probably want to speed up Earth's rotation (100x or 1000x) in order to more easily see the precession in a short time span. Pay attention to both the direction of the precession and the period of the precession. What is the difference in precession between the northern and southern hemispheres? What is the difference in precession between lower latitudes (like Bangkok) and higher latitudes (like Paris)?
• Now set the location to the equator. Watch the simulation with Earth's rotation set to different speeds. What happens to the precession at the equator?

Changing the Pendulum Length

• So far we have kept the length of the pendulum fixed at 16 m. Experiment with other pendulum lengths. Does changing the length of the pendulum change the precession period? What about the period of oscillation? (Hint: you can use the Time display to determine the oscillation period, which is the time it takes for the pendulum to complete one back-and-forth swing.) If either of these depends on the pendulum's length, how does it depend on the length?