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

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Discussion Overview

The discussion revolves around the physics of keeping a pencil balanced on a hand, focusing on the dynamics involved when the hand moves. Participants explore various physics topics relevant to modeling the pencil's behavior, including mechanics and uncertainty principles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests researching the relationship between hand acceleration and angle changes of the pencil, indicating a need for understanding dynamics.
  • Another participant introduces the Heisenberg Uncertainty Principle, arguing that even in an ideal scenario, the pencil would eventually fall due to inherent uncertainties in momentum and position.
  • A different viewpoint posits that if friction is considered, the effects of the uncertainty principle may be negligible.
  • Basic Newtonian mechanics and chaos theory are proposed as potential frameworks for understanding the problem.
  • One participant emphasizes the need for a deeper explanation of the scenario to provide more targeted advice.
  • Another suggests that introductory courses in statics and dynamics would cover the necessary principles for modeling the pencil's motion once it begins to fall.
  • There is mention of a specific problem related to the scenario being discussed in a physics text, indicating a connection to established academic resources.
  • A link to an external resource is provided, which may offer additional insights into the ideal conditions for the problem.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of the Heisenberg Uncertainty Principle and the role of friction, indicating that multiple competing perspectives exist regarding the physics involved in balancing the pencil.

Contextual Notes

Some assumptions regarding the ideal conditions of the pencil and hand are made, such as neglecting air motion and vibrations, which may limit the applicability of certain arguments. The discussion also reflects uncertainty about the specific mathematical relationships needed to model the scenario accurately.

Who May Find This Useful

This discussion may be of interest to those studying dynamics, mechanics, or anyone involved in programming simulations related to physical systems.

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

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.
 
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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
 


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.
 


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


you need to explain the situation more in depth
 


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.
 


Bob S said:
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?
 

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