- Why doesn't the pendulum's swing plane rotate at the equator?
- At the equator, the horizontal component of the Coriolis force—which is responsible for the sideways push on the pendulum bob—vanishes. The formula Ω_eff = Ω_E sin|λ| shows that when latitude λ is 0°, sin(0°) = 0, resulting in zero effective precession. The Coriolis force still acts vertically at the equator, affecting objects moving up/down, but it does not deflect the horizontal swing of a pendulum.
- Is the rotation of the swing plane proof that Earth rotates, and not that the universe rotates around us?
- Yes. The pendulum's behavior is most simply explained by assuming we are observing it from a rotating reference frame (Earth). In an inertial frame (like the distant stars), the pendulum's swing plane remains fixed while Earth rotates beneath it. The pendulum's motion is consistent with Newton's laws only if we include the fictitious Coriolis force, which is a direct consequence of our frame's acceleration (rotation).
- What simplifications does this simulator make compared to a real Foucault pendulum?
- This model ignores air resistance and damping, so the swing amplitude does not decay. It also treats the pendulum as a simple planar swing, neglecting the more complex 3D spherical pendulum motion that can cause elliptical orbits. Furthermore, it assumes a perfectly symmetric setup and a point-mass bob, whereas real pendulums require careful design and a driving mechanism to sustain oscillation.
- How does the precession rate change if I move the pendulum from the North Pole to a mid-latitude?
- The precession rate decreases as you move away from the pole. At the North Pole (λ=90°), the rate is maximum at 15°/hour. At a latitude of 45°, sin(45°) ≈ 0.707, so the rate is about 10.6°/hour. The sine function in Ω_eff = Ω_E sin|λ| captures this dependence, showing the precession is slower at lower latitudes until it reaches zero at the equator.