# NTNUJAVA Virtual Physics LaboratoryEnjoy the fun of physics with simulations! Backup site http://enjoy.phy.ntnu.edu.tw/ntnujava/

## Easy Java Simulations (2001- ) => Dynamics => Topic started by: Fu-Kwun Hwang on June 21, 2013, 11:40:45 am

 Title: in which direction will it roll? Post by: Fu-Kwun Hwang on June 21, 2013, 11:40:45 am If the spool is pulled horizontally to the right.in which direction will it roll?to the left?to the right?others ...Click the following image to show the simulation.[eye][ejsapplet][/eye] Title: Re: in which direction will it roll? Post by: Fu-Kwun Hwang on June 22, 2013, 09:30:12 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$$R*f-r*F=I*\alpha= I*\frac{a}{R}=\frac{I}{R} \frac{Fx-F}{m}=\frac{I}{m*R}(Fx-f)So (R+\frac{I}{m*R})f=(r*F+\frac{I}{m*R}Fx)=(r+\frac{I}{m*R}\frac{Fx}{F})*FWe will get f=\frac{r+\frac{I}{m*R}\frac{Fx}{F}}{R+\frac{I}{m*R}}*F$$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.[eye][ejsapplet][/eye] Title: Academic proofreading services Post by: rexujnk on August 11, 2014, 08:32:07 pm It's really dynamic theory, So nice.-*-