Galileo's Inclined Plane — Slowing Gravity Down
Free fall was too quick to time with the clocks of 1600, so Galileo diluted it: a polished groove, movable frets that click as the ball passes, and a water clock that weighs out the seconds. Tilt the groove and release the ball — the clicks stay evenly spaced in time while the frets sit at 1, 4, 9, 16, so distance grows as t² at every tilt right up to the vertical.
How to use this simulation
- Set the tilt anywhere from a gentle 3° up to a vertical 90°
- Press Release the ball and listen for evenly spaced clicks at the frets
- Load Galileo's gentle groove, then Steeper at 30°, then Stand it upright
- Switch to the water-clock view to see how the seconds were actually measured
What to look for
- The frets that give evenly spaced clicks sit at distances 1, 4, 9, 16
- Successive equal time intervals cover distances in the ratio 1, 3, 5, 7
- Steepening the groove speeds everything up without disturbing those ratios
- At 90° the groove is vertical and the motion is ordinary free fall
- A rolling bronze ball accelerates slightly less than a sliding one, but follows the same t² law
The physics behind it
On a frictionless incline of angle θ only the component of gravity along the slope accelerates the ball, giving a = g sin θ. That is a constant, so the motion is uniformly accelerated exactly as free fall is, just slower: s = ½at². Distances from rest therefore grow as the squares 1, 4, 9, 16, and the gaps between successive equal time intervals grow as the odd numbers 1, 3, 5, 7. Raising θ to 90° makes sin θ = 1 and recovers free fall itself, which is why the dilution changes the rate without changing the law.