[shamino]

Thanks for taking the time with me. Acceleration for me is a change in a velocity - isn't that what is going on ?

Velocity is a change in distance, and to me it seems there must be a change in distance - since there is energy being spent (we're "traveling" as we run, while putting in the force of our feet against the treadmill - each step is an "acceleration" forward).

[chrisseaton]

> Acceleration for me is a change in a velocity - isn't that what is going on ?

Yes that's what it is. But you aren't changing velocity when you start running on a treadmill. When you are on a treadmill your velocity is the same as a person standing still on the ground next to you. We may talk about you 'running at 5 mph', but this is just a casual way of talking unless you're doing a physics problem. In reality, your legs are moving in a similar way as if you were running at 5 mph, but your velocity, relative to when you started, is zero the whole time.

> it seems there must be a change in distance - since there is energy being spent

If you stand still and flap your arms you're spending energy aren't you? But you're not going anywhere. Next imagine running on the spot. Still spending energy but not going anywhere. Next imagine that on a treadmill. Still spending energy, still not going anywhere.

> we're "traveling" as we run, while putting in the force of our feet against the treadmill

Here's another way to think about it from scratch that may help.

You are running forward, going at 5 mph. The treadmill underneath you is going backward, at 5 mph. Your actual velocity is therefore 0, because the two cancel out.

When you run on the ground you are running forward at 5 mph, the ground is staying still, so the result is actually 5 mph.

People casually say that your velocity on a treadmill is 5 mph, but really they mean that you are moving your legs fast enough that you would be going 5 mph, if the treadmill was't working in the opposite direction against you. If you were doing a physics exam you would be more careful with your terminology and you would say that the velocity of someone on a treadmill is 0.

> each step is an "acceleration" forward

No, each step forward on a treadmill is compensation for the treadmill going backward. All of the progress forward that step gives you is used up balancing out that the treadmill is going backwards, and there is no acceleration.

[shamino]

Thanks very much for breaking it down for me.

I guess what I don't really understand is how I can tell the difference when I'm blindfolded.

If I am undergoing the same force with my feet on the treadmill than I do on the sidewalk, how do I really tell the difference ?

I know since the treadmill is moving on its own, I have to "walk" to keep up with it, but what if I could move the treadmill backwards as I walk ? (The force of my steps make the treadmill move, rather than the rotor machine?)

I understand I don't move anywhere with respect to the ground, but if I undergo the same motion that I do when I'm walking, how is it that I am able to tell the difference ?

If I can literally make the treadmill move under me just by walking, how is it different from walking on the sidewalk ?

Sorry - I'm just really baffled, even though I believe everyone. Could someone just ELI5 me ?

[chrisseaton]

The fluffy dice on a string.

Do you understand that when you accelerate in a car the dice moves toward the back of the car, so that the string leans backwards?

This happens because the car moves forward, but the dice wants to stay where it is. So it kind of gets dragged. This is a fundamental property of the universe we live in, called the first law of motion, and I can't explain that further as nobody knows why the universe is like the but it is.

Do you understand that this doesn't happen if you hold a fluffy nice on a string and run on a treadmill?

This happens because the dice wants to stay where it is, and it is staying where it is, so nothing happens. Whatever you legs are doing beneath the fluffy dice is irrelevant.

Your ear effectively has a tiny fluffy dice on string inside it, and tiny hairs that feel whether or not it is leaning backwards. You don't need to see or feel anything else to sense this, and it doesn't matter what your legs are doing. That's why the treadmill and your eyes don't matter. Your legs are running on it but the little dice in your ear knows what is really happening.

That is how you know that you are really accelerating.

And, going back to the original point, is the whole problem. There is no way to poke this fluffy dice to fake the sensation of acceleration, as it is sealed inside your head.

The fluffy dice in your head thing is obviously not quite true, but it really isn't that far from the truth.

You can do an experiment to understand this better (or at least prove it to yourself). Get a glass of water and half fill it. Get in a car and get a friend to accelerate somewhere legal and safe. The water will slosh to the back of the glass. This is like the dice. Now get a treadmill and turn it up high. Put the glass of water on the skateboard. Lower the skateboard on to the treadmill while it's still running. The 'acceleration' here will be huge as the skateboard will go from 0 to whatever mph instantly (it's not really acceleration, that's the whole point). The water will not slosh (if you put the skateboard down carefully).

[shamino]

Thanks, I think I finally get it - and the experiment would definitely confirm your point.

How does our inner ear chooses to uses the ground vs a point on the treadmill as it's starting point? I keeping wanting to think that I'm in motion with respect to a point on the treadmill.

What if your inner ear were located on your feet ? Would you then not be able to tell the difference between treadmill and sidewalk ? Your feet are actually traveling in the same motion on the treadmill as it would the sidewalk ?

[chrisseaton]

You are born onto the earth, so your reference point starts as the earth.

In reality the earth is moving through the solar system, so your starting reference point is in motion already.

If you get into a vehicle and start moving at speed relative to the earth, then that vehicle becomes your new reference point when the speed becomes stable.

When you step onto a treadmill your speed relative to the earth, your previous reference point, doesn't change, so the reference point doesn't change. If someone were to drag the treadmill behind a vehicle with you surfing on it, then it would become your reference point.

It's confusing to talk about your inner ear being in your feet because they're in a running motion, so they're being shaken up all the time. They'll experience constant acceleration and deceleration relative to the earth as your foot goes back and forward in a running motion. If you had little dice on strings in your feet you wouldn't be able to tell what was going on with them as the dice would be flapping all over the place.