How to Calculate the Minimum Couple to Rotate a Cylinder on Inclined Planes

[Johnny87]

A uniform cylinder of radius a and weight W rests in equilibrium between 2 rough planes which are both inclined to an angle pi/6 to the horizontal. The axis of the cylinder is parallel to the line joining the two planes and the coefficient of friction at both points of contact is 1/2.

Find the least couple which must be applied to the cylinder to make it rotate.




Please help me! Who knows how this can be done?

 

[einstein_a_go_go]

Construct a diagram of the forces before the cylinder rotates. Resolve forces and find the normal reactions.

The draw the diagram again for the block in rotation...you know the weight and normal forces, so you can find out the Friction forces and hence the couple...

Diagrams are the answer.

 

[Johnny87]

The problem is I don't know how to draw the diagram.. For example, which axis of the cylinder is it talking about? (Cylinders have more than one axis, if I'm correct)
I'm really confused.

 

[katchum]

Cilinders have only one important axis. The other two are of no importance.

 

[Johnny87]

Which is..?

 

[katchum]

The one that determines the rotational vector of a 'common' rotating cilinder wheel.

You know, the one that goes throught he center of the cilinder?

 

[einstein_a_go_go]

always go for the simplet solution - imagine a vee shape. in the vee is a circle. this is an end on view