Calculating Torque for Rotating Cylinder in V Groove

[Kurret]

Homework Statement

A cylinder of mass M and radius R is rotated in a uniform V groove with constant angular velocity w. ( the V groove is symmetric with a 90 degrees V, and 45 degrees on both sides of the V to the horizontal plane). The coeff. of friction between the cylinder and each surface is f. What torque must be applied to keep it rotating?

Homework Equations

t=fxR

The Attempt at a Solution

The keep it rotating with constant angular velocity, the net torque must be zero. The torque from the friction for each side of the V is R*f*Mg/Sqrt(2), so the total torque should be Sqrt(2)*RfMG. Thus we must apply the same torque to keep it rotating.

Now this seemed too good to be true, and it certainly was. The answer should also be divided by (1+f^2). Why?

 

[tiny-tim]

Hi Kurret!

Call the two normal forces N and M, draw in the friction forces, and take componenets both horizontally and vertically to find N and M.

 

[Kurret]

Thanks Tim! :)

 

[Kurret]

But, when we apply the torque, will not the force from the torque we apply also affect the normal forces?

 

[davieddy]

No. Assume that the torque is applied by a "couple".