Treadmill hypothetical

The only confounding issue here is that human legs are a complex system for moving something forward.

In terms of momentum:

When you’re running on a treadmill, you’re stationary with respect to the ground - if the treadmill suddenly vanishes, you don’t shoot forward. Your legs start to try to move you forward, but in practice, you probably stumble, maybe injure your ankles and knees, maybe fall on your ass - at best you end up standing still wondering what the hell happened.

Simplify the system to a motorbike on a treadmill (wheels are simpler than legs) - if the treadmill stops or vanishes, the wheels spin on the stationary surface and the motorbike begins to accelerate forward with respect to the ground. It doesn’t instantaneously start moving forward at the speed it was running on the treadmill.
The rider of the motorbike, in this scenario, feels the tug of acceleration just like he would with a standing start. If the engine is powerful and the wheels really grippy, the motorbike runs away from underneath the rider and he falls on his ass.

This seems trivial to actually test and gather empirical data. Being a red blooded american my treadmill is, of course, covered in laundry so I’m unable to test it myself. Surely someone has a functional treadmill and can test it?

For the treadmill, when someone jams it to make it stop, your body is stationary with respect to it, even though your legs are moving. You’d have to accelerate to continue running on the ground instead.

When you first step onto the moving walkway, your body is stationary with respect to it, even though your legs are moving. You’d have to accelerate to continue running on the walkway instead.

It can be approximated by just jumping off the side whilst running at full speed, but the physics (apart from the mechanics of the legs) is really very straightforward.

I can second this.
I had a treadmill stop; in my case the belt just stuck for a fraction of a second, then continued. I too fell forwards. My legs went out from under me and the only thing that stopped me falling flat on my face was that I grabbed the bar.

For some reason I didn’t think to hit the stop button but tried to just roll off the machine…got myself some surprisingly nasty cuts for my trouble.

But, as to why I fell…a lot of it was the disorientation, and not knowing where to put my next stride. Perhaps with practice you could continue running smoothly through such an event?

To continue running smoothly would require your body to instantly accelerate to the speed at which the treadmill was formerly moving, which isn’t possible. With practice you could probably learn to quickly adjust and avoid a tumble, but it wouldn’t be a smooth unbroken stride.

If your reflexes are good enough, you’ll break your stride and end up standing in place. If your reflexes aren’t good enough, then you’ll fall onto your back.

Thinking about it more I think it would depend on where you were in your stride.
As you run your body remains stationary as each foot takes turns planting out front of your center of gravity, traveling backwardward underneath your center of gravity, and then finally lifted off the ground behind your center of gravity.
If the treadmill came to an abrupt stop when your foot is planted ahead of you I’d expect you to fall backward. If it stopped when your foot was planted behind you I’d expect you to fall forward. Somewhere underneath you you may have a good chance of catching yourself standing.

In my treadmill stop it stopped as my forward foot planted and I fell forward onto my leading leg.

Again, I think it about what pattern we are expecting to activate and how we respond when that circumstance does not occur. I was, subconciously, expecting that foot to be dragged backwards and planning to keep my center of gravity leaned just enough to stay over it as it did so. But not enough to drive forward over that leg of my own force and to have my center of gravity far enough forward to catch myself on my other leg. When it did not happen I think I tried to compensate and lean forward - hence collapsing onto my leading leg. Without that attempt to compensate I think the physics would have had me just fall straight down as my center of gravity was set back to where I was expecting my leg to be that microsecond, not over where my foot had stopped, so fall down (not back).

Definitely did not fall backward. Definitely could not have kept running forward.

When I accidentally hit the emergency stop button on the treadmill, I end up moving forward and slamming into the bar. However, 1) I’m seldom running full sprinting speed, and 2) the bard is less than two feet from my chest. I suspect that if I were going faster and didn’t have something to slam into/grab onto, I’d end up on my back.

That happened to me IRL. Yes really. While I appreciate the theories above, no one realizes that humans actually have good reflexes and can stop, suddenly. Which is what I did. I did have a bit of a run on, but it wasn’t much. My brain engaged with, ‘hey stop running, the treadmill quit’. Now, full disclosure-- my treadmill had a belt problem which I didn’t get around to fixing for a while so after the first time this happened, I kinda started to expect it, but the first time, I remember it clearly. I gave a slight lurch and two steps forward, and grabbed the front console to steady myself.

Human reaction time really is quite a lot better than most folks realize.

My experience was not a theory; I really did fall over. Also drewtwo99. So maybe we can conclude that human reactions are really quite poor in some cases.

However, I only do fast speeds on treadmills (I just use them for warming up prior to working out). When it happened I probably had it set to about 12.5 km/h (=7.7 mph)