/sci/ - Science & Math

And yet it moves faster than light /sci/

And yet it moves faster than light /sci/

I have a couple of questions about Galileo's work.

He used an inclined plane to test the properties of bodies as they fall, because he couldn't accurately measure a falling object's position after an certain amount of time, especially considering he was using pendulums/dripping water clocks and had no access to things like high-speed cameras. Fair enough.
But
Is an object rolling down a slope a good model for an object in freefall? Even if we ignore the effect of friction and assume air resistance to have the same effect on both, does an object on a slope 'fall' at the same rate as an object dropped?

While this makes sense to me logically, since g is constant, I can't see it working in practice.

Suppose a frictionless surface at an angle of, say, one degree from the floor. The surface is long enough that the other end is raised by 10cm. Surely a ball will fall 10cm faster than it would roll down a slope that long? In a model like that, it just doesn't make sense to me. What if the slope was one arcminute from the floor?
Also galileo had no frictionless surface, so how could his models be considered accurate? Is this only because he was comparing objects under the same conditions so it was irrelevant?

No.