What is the direction of friction on a plate on two rotating wheels?

[lavankohsa]

Homework Statement

A uniform plate of mass M stays horizontally and symmetrically on two wheels rotating in opposite
directions. The separation between the wheels is L. The friction coefficient between each wheel and the plate is N. Find the time period of oscillation of the plate if it is slightly displayed along its length and
released.

http://[PLAIN]http://i61.tinypic.com/25thrlw.png
2. Homework Equations

My teacher solved this problem in class and i understood everything except the direction of friction. The plate moved to right by distance x.

http://[PLAIN]http://i61.tinypic.com/ixwpci.png

The Attempt at a Solution

According to me right wheel should have direction of friction inside. Because plate wants to move out. So it will try to move back the plate left side.

 

[Tanya Sharma]

According to me right wheel should have direction of friction inside. Because plate wants to move out. So it will try to move back the plate left side.

How would the topmost point of the right wheel move with respect to the plate above it ? Towards right or left ?

 

[lavankohsa]

i figured it out the my own. i thought that he is displacing the plate right while maintaining the contact with rotating cylinder. But He is lifting the plate, displacing it and then putting it back.