Izbrane teme sodobne fizike in matematike
Članek z elementarno matematiko in fiziko razišče vrtenje nihajne ravnine Foucaultovega nihala. Kot zasuka ravnine poveže z geometrijo gravitacijskega polja Zemlje, katere površje je v približku popolne sfere ekvipotencialna ploskev polja. Izpelje odvisnost kota zasuka od geografske širine nihala in trajanja opazovanja. Z Gauss-Bonettovim izrekom iz diferencialne geometrije nato izsledke kratko posploši na ekvipotencialne ploskev poljubnih polj v prostoru.
The article examines the rotation of the swing plane of the Foucault pendulum. It employs only elementary mathematics and physics. It relates the angle of rotation of the plane to the geometry of the Earth’s gravitational field, which is in the approximation of a perfect sphere an equipotential surface of the field. The magnitude of the rotation is expressed as a function of geographical latitude of the pendulum and length of the observation period. Finally, using the Gauss-Bonnet theorem of differential geometry, the results are briefly generalised to equipotential surfaces of arbitrary fields space.