"Keeping a pencil standing on your hand" What physics topics should I research?

[lgmcben]

Hi.

My English is not perfect but I'll try my best. This is not a homework. It's a programming question for my simulator project.

Scenario:
- A pencil standing in your hand. It will fall or stand depending on how you move your hand.
- Let's assume that the hand is just an ideal 'plane'.
- Let's assume that a pencil is just a simple, ideal rectangular rigid body object.
- *** Let's assume that a pencil will NOT fall on y-axis. Or in English: It will only fall to the left or right.


Variables I have:
- Real-time 'Acceleration' of my hand in x axis. (in m/s/s)
- 'Mass' and 'Volume' of a pencil.

Variables I need:
- The change of 'theta'(angle) between the pencil and my hand(in x-axis) in each time slice. Or you could say d(theta) by d(t)

Questions:
What topic should I research for to relate the acceleration to the angle changes?


note:
*** Actually I want to do x,y and z axis but I think if I know how to solve one, I should be able to solve other too.

Thank you in advance! Please let me know if I didn't provide enough information to the problem.

[Bob S]

If the pencil were perfectly balanced on its point on an ideal stationary plane (no vibration) and there was absolutely no air motion, the pencil would still fall over in a few seconds, due to the Heisenberg Uncertainty Principle. The combination of Δp (momentum) and Δx (position) in

Δp Δx ≥ h-bar/2 means that if the initial (angular) position is fixed, the uncertainty in (angular) momentum will cause the pencil to fall over.

Bob S

[Pinu7]

Bob S is technically correct. However, if you consider a SMALL amount of friction between the pencil and the pivot, then Heisenberg's Uncertainty Principal can be neglected.

First, you must tell us the mass-space distribution of the pencil.

[Phyisab****]

Either basic newtonian rigid body mechanics, or chaos theory. Not sure which one you're getting at here.

[dacruick]

you need to explain the situation more in depth

[Naty1]

lgm..What topic should I research for to relate the acceleration to the angle changes?

the above replies seem focused on the initial instability...but

you do have enough information to develop a formula for the movement of a pencil once it begins.

Likely any introductory college course in statics and (you want this) DYNAMICS would discuss such a falling lever scenario. You'll want to relate the acceleration of the center of mass of the pencil downward from a formula like F = Ma to the movement about the base of the pencil.....the vertical (y) movement is obtained from an equation such as d=1/2at2 and I think, but am not sure, that the falling motion of the center of mass is independent of the one pencil end being "anchored"....it's been too many years since I did those kind of problems....

anyway, the above should get you started. good luck.

[xlines]

If the pencil were perfectly balanced on its point on an ideal stationary plane (no vibration) and there was absolutely no air motion, the pencil would still fall over in a few seconds, due to the Heisenberg Uncertainty Principle.
...

Bob S

That problem was given in Sakurai, but I got 6 minutes for "reasonable" measures of icepick.
Did you estimate that or did you actually did the math?

[DocZaius]

You could take a look at this page for a more ideal setup than the one you describe. I'm sure it would be helpful to you.

http://www.mathpages.com/home/kmath259/kmath259.htm