Imagine, if you would, that you have a cylinder of, say, 4 ft diameter (for the sake of argument … could be any diameter)
This cylinder has a tapered hole machined in the center of the peripheral curved surface, into which a matching tapered plug is inserted which is held in place by friction.
It has been experimentally established (by spinning the cylinder in a lathe) that when, and not until, the peripheral speed reaches 100 mph, then the tapered plug dislodges, due to the centrifugal force exerted.
Now further imagine that you have an immensely long ramp, long enough and with a steep enough incline that when you roll the above cylinder down it, the peripheral speed of the cylinder reaches 100mph.
My question is whether the same centrifugal force is exerted when the cylinder rolls as when it was rotated between two fixed centers … will the tapered plug shoot out just the same as before ?
On a lathe, or horizontal surface, the force exerted on the plug is proportional to the sum of the centrifugal acceleration and the acceleration from gravity. Assuming the conditions are perfect, and the cylinder has its rotation rate increased slowly, the plug will always be released at the bottom since that is the point of maximum gravitation acceleration (assuming the plug always separates radially).
On a ramp, though, the cylinder is accelerating down. Not at the full 9.8 m/s^2, but at some value. Hence, you’ll need to spin the cylinder faster for the plug to feel the same net acceleration as in the static case.
Let’s assume the ramp is two rails so that the plug is never pushed on by the ramp as the cylinder rolls, and that there is no frictional heating of the cylinder, and all those other nice first-year physics problem set assumptions.
If the cylinder were rolling along at a constant 100 mph, then yes the plug should pop out as we could examine the problem in the inertial frame of the cylinder itself. If the cylinder is rolling downhill and accelerating, I’d assume it works about the same, and I suspect you’d need pretty fine instruments to measure the difference due acceleration.
You’ll need to be more precise about “peripheral speed”. Is this the speed of a point on the edge of the cylinder with respect to (a) the center or (b) a point on the opposite edge of the cylinder ?
(a) is the only sensible interpretation when the cylinder is spun in a lathe. But when it’s rolling downhill (b) could make sense. (a) implies twice the rotational speed - RPM - of (b), and centrifugal force (which is what will dislodge the plug) is proportional to RPM squared.