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?

  • $\begingroup$ You might do some research on gun barrels with an outer and an inner. $\endgroup$ – user207455 May 27 '19 at 14:21
  • $\begingroup$ 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!!). $\endgroup$ – user220805 Aug 6 '20 at 12:41

My experience is that the rubber band stick to the cylinder and it is impossible to get uniform tension. I warmly recommend to find a rubber band and do the experiment!

You should get a radial force proportional to the local tension, plus a tangential force from friction that compensate the non-uniform tension. For thin rubber band, I will say that the tangential force is proportional to the gradient of the tension.

  • $\begingroup$ The gradient relates to the idea that friction will cause the tension to decrease as you go around the cylinder in the direction of rotation. $\endgroup$ – R.W. Bird Dec 7 '20 at 15:26

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