Derivation for Friction in Brakes

[plutamech]

Homework Statement

Derive the expression for frictional resistances in block brakes.Use standard symbols to denote required parameters.

Homework Equations

The Attempt at a Solution

My actual problem is the fact that I have checked 2 reference books, both have derived the expression assuming the friction produces a torque in the same direction of rotation of the drum.There is no explanation why this has been done.
If these 2 forces(friction and force of rotation) were to produce torque in the same direction then I suppose the drum should never stop its rotation, so what is the actual derivation with explation?
Kindly Help..

 

[plutamech]

I have got the answer to my question.
Thank You Physics Forums.