3.7 A test of the principle of inertia by Benjamin Crowell, Light and Matter licensed under the Creative Commons Attribution-ShareAlike license.

## 3.7 A test of the principle of inertia (optional)

Historically, the first quantitative and well documented experimental test of the principle of inertia (p. 80) was performed by Galileo around 1590 and published decades later when he managed to find a publisher in the Netherlands that was beyond the reach of the Roman Inquisition.^{1} It was ingenious but somewhat indirect, and required a layer of interpretation and extrapolation on top of the actual observations. As described on p. 97, he established that objects rolling on inclined planes moved according to mathematical laws that we would today describe as in section 3.6. He knew that his rolling balls were subject to friction, as well as random errors due to the limited precision of the water clock that he used, but he took the approximate agreement of his equations with experiment to indicate that they gave the results that would be exact in the absence of friction. He also showed, purely empirically, that when a ball went up or down a ramp inclined at an angle `theta`, its acceleration was proportional to `sin theta`. Again, this required extrapolation to idealized conditions of zero friction. He then reasoned that if a ball was rolled on a *horizontal* ramp, with `theta=0`, its acceleration would be zero. This is exactly what is required by the principle of inertia: in the absence of friction, motion continues indefinitely.

3.7 A test of the principle of inertia by Benjamin Crowell, Light and Matter licensed under the Creative Commons Attribution-ShareAlike license.