### Author Topic: in which direction will it roll?  (Read 10824 times)

#### Fu-Kwun Hwang

• Hero Member
•     • • Posts: 3062 ##### in which direction will it roll?
« on: June 21, 2013, 12:40:45 pm »  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 ...

4. Click the following image to show the simulation. Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
• 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!  #### Fu-Kwun Hwang

• Hero Member
•     • • Posts: 3062 ##### Re: in which direction will it roll?
« Reply #1 on: June 22, 2013, 10:30:12 pm »
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   heta-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. Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
• 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!  #### rexujnk

• Newbie
• • Posts: 1 