Howdy,
I think the subject is sort of clear. All that took place, say, as the last two escalator steps disappeared at the top landing.
I thought that that would be a standard undergraduate analysis problem in physics: dynamics, right?
I’ll have more questions I’m sure once somebody comes along … 
I cannot figure out your subject. “Holding on” to what, the railing? What do you mean by “pivot”, are you talking about rotating on one planted foot? Which direction are we pivoting and by how much, and by what means–pushing off from the railing? What are you pushing after the pivot and for what purpose? What is accelerating, have we pushed ourselves forward or something? What do you mean by pivot right?
Most importantly, what is the problem that would be solved from this setup? I only see a description of actions that take place. What are you trying to figure out?
OK, I deserved that. My apologies.
“Holding on” to what, the railing?
Yes. So I’m giving myself a boost with my arms on a moving something, and I’m thinking about how that boost manifests itself through time in one direction relative to myself, the escalator relative to itself, and relative to the stable floor I am about to negotiate.
My thoughts while finishing all the actions described below: 1) I wonder if this is what the guys at JPL think about when bouncing satellites or whatever; 2) I wonder if this has the slightest relation to what atomic physics people think about all day, but with hundreds more, I don’t know, “more dynamics shit” going on.
Third thought: must ask SD folk.
This is sort of a beginning to your final query, which I address in turn below.
What do you mean by “pivot”, are you talking about rotating on one planted foot?
Yes.
Which direction are we pivoting and by how much, and by what means–pushing off from the railing?
Two pivots: 1) on my right foot anticipating as steep as possible right turn, then 2) my left foot alights and my body continues traveling as I pivot trying to go 180° of the direction of the escalator.
What are you pushing after the pivot and for what purpose?
See above. 1) the railing and the floor, and I guess whatever internal muscolosketal systems for the torque.
What is accelerating, have we pushed ourselves forward or something? What do you mean by pivot right?
I think it should be clear from the above, but of course I will try to make it clearer if you want.
Most importantly, what is the problem that would be solved from this setup? I only see a description of actions that take place. What are you trying to figure out?
Well, that’s an important question. It’s like this:
This post is #3532 in a seemingly unending series of mine in which I try to get a feel (as it were) of how a physicist uses a) words/concepts about which I haven’t the faintest, or b) “know” about–such as acceleration, angular moment, and some others–which are part of most educated high-school graduates (if they remember), but I, for one, cannot dope out what is truly pertinent (the “set-up” in my hed) and, something which gives me pleasure from learning–thanks to the good 'ole boys in GQ–when values are placed on the pertinent factors and worked out.
A little bleg for a blackboard illustration. Sometimes I have a hankering for exactish numerical values just to be goofy, thought-provoking, and tweak the physicists here (like so many fun posts).
Other times, if I believe the problem is workable-outable on a level commensurate with many other type posts here (“Trying to explain to my kid about…”) I look toward to (but won’t pout if nobody feels like doing it) a working through of the math either as shown or what is far often the point of my questions to see a “working out”, if someone says, eg, “here we do a Fourier transform, just trust me,” I can add that to my understanding of the way/what/when/how a FT is supposed to work.
If I’m reading you right, you’re basically saying, “You’ve got someone jumping/thrusting/pushing themselves off an upward-going escalator such that they land firm on the ground facing back toward the escalator. Discuss, in a physics-y way.”
If so, here are a few thoughts…
The torque/rotation systems you get in high school physics all have symmetries and/or constraints that make the math easy. In these problems, the applied torque gives rise to a change in angular momentum which in turn is related to the angular velocity (i.e., the rotation speed) by a constant factor determined by the mass distribution of the object (the moment of inertia). Homework problems consist of calculating moments of inertia of differently shaped objects, or figuring out how fast something is spinning after a torque has been applied for a while, or using conservation of angular momentum to figure out what a system is doing after some torque-less change has occurred.
As soon as you remove the symmetries and rotation constraints, things get messy fast. A general object rotating in 3D – even without external torques applied – must be described by a moment of inertia tensor, which requires six numbers to fully specify. For a rigid object, this tensor is constant in the object’s co-rotating reference frame, but in an external observer’s reference frame, the tensor is changing since the object is rotating. Since the momentum of inertia tensor is what relates angular momentum to angular velocity, then that relationship is constantly changing. Thus, even in the absence of external torques (i.e., constant angular momentum), a general 3D object rotating in empty space can already have some complicated motion.
For a quick example of this even for a system with some symmetries, take a rectangular object with different height, width, and depth. (A book with a rubber band holding it closed, or a scrap of wood, or a remote control.) There are three symmetry axes you can flip the object around. Around two of these axes, you can get stable rotation. Around one of these axes, you cannot. You will find that the rotation quickly turns into a complicated mess when you try to flip the object through its “intermediate” axis (as opposed to its long axis or short axis).
Fast forward to your system. You’ve got torque applied from three places (hand, hand, foot) and you’ve got an object that isn’t internally rigid, as there are internal forces, torques, and degrees of freedom with the body (all of which are notably underspecified in the problem as stated). To be sure, the physics behind all this is straightforward, but one would be daft to approach this analytically(). Rather, this is a prime case for numerical methods, which is how 3D rotations of complex objects are in fact dealt with in practice. You step the system through tiny steps, calculating how things are changing and where they end up after each step, until you get the system all the way to the end point.
() “analytically” here meaning, roughly, “on proverbial pen and paper alone, toward a closed-form description”
The point at which one ceases to be aboard the escalator and transitions to being aboard the landing is continuous but not differentiable. It follows that any body making that transition will be rent asunder at that point.
It only works due to the inherent squishiness of the people using the escalator.
(I am reminded of an actual calculus problem: A road has a 90-degree curve in it. The road has straight stretches approaching the curve in both directions, but the curved part itself is a 90-degree arc of a circle. Criticize the design of this road.)
It’s not often in GQ that I get to describe something as infinite jerk!
Is that like being reminded of a nightmare ?