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Author Topic: in which direction will it roll?  (Read 2156 times)
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Fu-Kwun Hwang
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on: June 21, 2013, 11:40:45 am » posted from:,,Satellite Provider


    If the spool is pulled horizontally to the right.
      in which direction will it roll?

      1. to the left?
      2. to the right?
      3. others ...



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* rotatingCylinder.jpg (30 KB, 823x427 - viewed 158 times.)
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Fu-Kwun Hwang
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Reply #1 on: June 22, 2013, 09:30:12 pm » posted from:,,Satellite Provider

Here is another more general case: You can drag the Force arrow to change it's direction.


1. Choose the center of the disk as origin.
Assume the friction force is f, The x, y component of the external force F is Fx, Fy

Then from Newton's law: Fx-f=m*a
The Net torque is R*f-r*F=I*\alpha
Assume the disk motion satisfy "Rolling Without Slipping" condition: i.e. a=R*\alpha

R*f-r*F=I*\alpha= I*\frac{a}{R}=\frac{I}{R} \frac{Fx-F}{m}=\frac{I}{m*R}(Fx-f)
So (R+\frac{I}{m*R})f=(r*F+\frac{I}{m*R}Fx)=(r+\frac{I}{m*R}\frac{Fx}{F})*F

We will get f=\frac{r+\frac{I}{m*R}\frac{Fx}{F}}{R+\frac{I}{m*R}}*F

I*\alpha=R*f-r*F=R*\frac{r+\frac{I}{m*R}\frac{Fx}{F}}{R+\frac{I}{m*R}}*F-r*F=\frac{R*r+\frac{I}{m}\frac{Fx}{F}-r*R-\frac{I}{m}\frac{r}{R}} {R+\frac{I}{m*R}}*F=\frac{R*\frac{Fx}{F}-r}{I+m*R^2}*F=\frac{R*\cos\theta-r}{I+m*R^2}*F

I+m*R^2 is the new "Moment of inertia" if we move the origin to the point disk in contact with the surface.


Click the following image to show the simulation.

Embed a running copy of this simulation

Embed a running copy link(show simulation in a popuped window)
Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License
  • Please feel free to post your ideas about how to use the simulation for better teaching and learning.
  • Post questions to be asked to help students to think, to explore.
  • Upload worksheets as attached files to share with more users.
Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!


* rotatingDisk.gif (3.62 KB, 349x267 - viewed 125 times.)
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rexujnk
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Reply #2 on: August 11, 2014, 08:32:07 pm » posted from:,,Satellite Provider

It's really dynamic theory, So nice.-*-
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