Celestial mechanics and terrestrial physics
If you let a heavy pendulum swing freely in Bucharest, its oscillation plane completes a full rotation in 34 hours and 17 minutes. This rhythm seems to contradict the 24-hour rotation of the Earth: in reality, the pendulum preserves its direction relative to the stars, while the floor of the room turns beneath it at 10.50 degrees per hour.
Select a location or adjust the latitude slider to observe the needle tracing its rosetta and knocking down the perimeter reference pins.
A pendulum suspended from a gimbal joint receives no horizontal torque from the building. Once set in motion, the first law of mechanics forces it to preserve its plane of oscillation in inertial space. To an observer standing on the floor, the needle appears to drift slowly to the right, but viewed from space the pendulum swings along a constant line, while the city turns to the left beneath it.
The rotational speed of the floor depends strictly on the sine of the latitude. At the North Pole, the floor sits perpendicular to Earth's rotation axis, completing a 360-degree circuit in 24 hours at 15 degrees per hour. At the Equator, the floor is parallel to the rotation axis, meaning the vertical rotational component is zero: the needle swings along the same line indefinitely. At the latitude of Bucharest, the sine of 44°26' is exactly 0.7001, lowering the hourly speed to 10.50 degrees and extending the complete cycle to 34 hours and 17 minutes.
Because Romania spans nearly four degrees of latitude, the pendulum day varies measurably across the country. In Craiova and Bucharest, a complete cycle takes 34 hours and 17 to 21 minutes. In Timișoara and Sulina it drops to 33 hours and 30 to 51 minutes, in Cluj it reaches 32 hours and 56 minutes, and in the far north, in Botoșani, it comes down to 32 hours and 25 minutes. Traveling from the Danube to the northern border shortens the pendulum day by nearly two hours.
| Location | Latitude | sin(φ) | Angular Velocity | Full Period (360°) |
|---|---|---|---|---|
| Bucharest | 44.43° N | 0.7001 | 10.50°/h | 34h 17m |
| Craiova | 44.33° N | 0.6988 | 10.48°/h | 34h 21m |
| Sulina | 45.16° N | 0.7090 | 10.64°/h | 33h 51m |
| Timișoara | 45.75° N | 0.7163 | 10.75°/h | 33h 30m |
| Cluj-Napoca | 46.77° N | 0.7286 | 10.93°/h | 32h 56m |
| Iași | 47.16° N | 0.7333 | 11.00°/h | 32h 44m |
| Botoșani | 47.75° N | 0.7402 | 11.10°/h | 32h 25m |
| North Pole | 90.00° N | 1.0000 | 15.00°/h | 24h 00m |
| Paris (Panthéon) | 48.85° N | 0.7529 | 11.29°/h | 31h 52m |
| Quito (Equator) | 0.00° N | 0.0000 | 0.00°/h | Never |
| Sydney | 33.87° S | -0.5573 | 8.36°/h | 43h 04m |
In February 1851, French physicist Léon Foucault suspended a 28-kilogram brass bob from a 67-meter steel wire beneath the dome of the Panthéon in Paris. On the floor, he placed a circular ring of moist sand and a series of wooden pegs. The stylus mounted at the bottom of the bob grazed the sand with every swing, proving directly and without astronomical observation that the planet rotates beneath the feet of onlookers.
The pendulum day is calculated using Foucault's sine law, T = 24 / sin(φ), where φ represents geographic latitude referenced to the WGS 84 ellipsoid. Angular hourly velocity is derived from Earth's rotation rate (15 degrees per hour of sidereal time). Geographic coordinates for Romanian localities come from the official geodetic registry.
The interactive dial integrates coupled harmonic equations in the local reference frame, computing the hourly azimuth drift and physical contact with 36 perimeter pins spaced at 10-degree intervals.