"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..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

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