# Pressure of rubber band on cylinder taking friction into account

Suppose I have stretched a rubber band around a cylinder of radius $$R$$ such that the rubber band is under tension $$T$$. My understanding is that in the ideal situation, with no friction, the band applies a force per unit length of $$T/R$$ radially to the cylinder. If the band has width $$W$$ and everything is uniform then it exerts a pressure of $$T/RW$$ to the cylinder. This is based on my own reasoning (though I haven't done any physics problems like this in over a decade), and some online sources:

This one says $$4T/2\pi$$ (so it does not depend on $$R$$) but I think that is incorrect (please correct me if I am wrong): Elastic band around a cylinder

My question is how does this change (if at all) if the friction between the rubber band and the cylinder is taken into account?

• You might do some research on gun barrels with an outer and an inner. – user207455 May 27 '19 at 14:21
• Your answer is correct, both radial force per unit length and pressure. I believe $\frac{4T}{2π}$ refers to something else (It has units of force!!). – user220805 Aug 6 '20 at 12:41