The Clutch Effect

I'll start from the familiar, then delve into the implications.

You have a stack of paper, with a sheet near the bottom peeking out.  You grab that, and pull gently and slowly; the whole stack moves towards you.  You grab it and pull hard and fast; just that sheet emerges, leaving the rest of the pile where it is.

So you scale that up to the "tablecloth trick".  Disaster!

You have an old car with a shot clutch.  If you accelerate slowly and gently, the clutch "works" and the car accelerates proportionally in line with your expectations, based on the engine's revs and selected gear.  But if you stomp the gas, the engine revs speed up nicely but the car doesn't move much faster.

You have Diabetes Mellitus ("peeing lots of sweet urine", as per the tyranny of the measurable... a topic for another day). If you digest carbs slowly, you may be OK; if you digest fast, less so.

You're piloting a fighter aircraft, pursued by a guided missile, and you try to turn and climb to evade it - but at 9G, you black out.  The human-free missile has no such limitations.

You're a 1kg block of whatever, moving through space a nudge above zero.  Your experience is vastly different to that of a similar block moving a nudge below c.  See "The universe has two speeds c, and zero; everything else is just a rounding error" for that and more.

You're a man carrying a bucket of water, and at that familiar scale, a liquid generally sinks to fill a container, with a flat surface on top that usually curls upwards a bit round the rim, unless it's mercury, which curves downwards instead.  Contrast that with an ant carrying a bead of water; though the scale isn't that much smaller than our familiar, the experience is already very different, and the opposite of how liquid helium climbs out of its container.

You're a steady DC current, flowing effortlessly through a coil but stopping dead at a capacitor.  You're perfect (i.e. highest frequency) AC, skipping effortlessly across a capacitor but stopping dead at a coil.  So far, so good... now you're a bolt of lightning striking a phone line, frying almost everything in an old 286 PC, yet the monitor remains unscathed - because the 90 degree bend of the thick copper wires at the graphic card's signal port melted before the current to reach it.  What's going on here, if lightning is DC?  Yes, but that very fast rise time behaves more like perfect AC... so to protect against lightning, tie knots in your cables - big ju-ju, works good!

What's common to all these scenarios that I've clumped together as "the clutch effect"?  It ties in with layers of abstraction, within which certain models work (e.g. Newtonian motion and speeds near 0) but beyond which, different models may be needed (e.g. Relativity at speeds near c).