foucault

a pendulum that knows what latitude it is

— observing from above —
elapsed0 h
rotation0.0°
latitude 48.86° N
time scale ×2000
period 31.8 h
custom latitude
rotation rate vs. latitude 11.32°/h
latitude -+ time scale space pause R reset

A pendulum hung from a long enough wire, set swinging in a straight line in one plane, will appear over the hours to swing in a different plane. The pendulum has not changed plane. The Earth has rotated underneath it, and the swing plane — fixed with respect to the distant stars — is the part of the apparatus that didn't move.

The plane appears to rotate at ω = ω_E · sin(latitude), where ω_E is one full rotation per sidereal day (23 h 56 min 04 s). At the pole this is one full rotation per day. At the equator it is zero. In between is the bit Léon Foucault demonstrated to the public at the Panthéon on 26 March 1851, hanging a 28-kilogram brass bob from a 67-metre wire under the dome. The exhibition has, intermittently, never closed.

The compass rose here is fixed to the ground, like the marble inlay below the original Panthéon installation. Watch the swing plane drift relative to it. Northern hemisphere: clockwise as viewed from above, the direction the ancients called deasil. Southern hemisphere: counter-clockwise, widdershins.

The chart below plots that same relationship directly — hourly rotation rate as a function of latitude, a plain sine curve peaking at ±15.04°/h (one sidereal rotation, spread over a day, at the poles) and crossing zero at the equator. Every preset above sits on it as a small dot; drag the chart itself to set latitude the same way as the stage or the slider. Whatever latitude and time scale you leave the page on will still be there next time you open it.