Twisting a tightly fitting rod Consider the task of extracting a cylindrical rod held by friction in a tightly fitting shaft. Instinctively one would tend to twist the rod around its axis while pulling. The question is,  what is the physical basis for this? Does applying a torque reduce the axial force required? 
 A: When you pull on the cylinder you apply a force $f_\mathrm{pull}$ between the rod and the shaft. When you twist you apply an additional force $f_\mathrm{twist}$ which acts perpendicularly to $f_\mathrm{pull}$. The total force acting between the rod and shaft is then $\sqrt{f_\mathrm{pull}^2+f_\mathrm{twist}^2}$ which is greater than $f_\mathrm{pull}$ alone.
Why does this help remove the rod? Because the larger force helps you overcome the stiction and thus enables the rod to move.
A: Can we assume that this a non-deformable problem? i.e. Are we talking about something like a metal rod inside a metal tube? If the materials are deformable - e.g. a wine cork in a bottle, then I think there are all sorts of factors to do with the elastic properties of the material that come into play.
So leaving that aside; applying a torque to the stuck item will provide a force that may be able to overcome the static friction, without applying a further normal force to the sides of the tube that might increase the total force required to get the thing out. The problem with just pulling is that inevitably the force is applied non-axially, or the tube is not precisely straight and so an additional, possibly very large, normal force is applied to points along the tube which in turn increases the force required to overcome static friction.
A: I agree with @lemon that the torque may help overcome static friction, however, his/her formula does not look convincing, as, if we applied both forces in the same direction, we would increase the magnitude of the total force.
My hypothesis is if you use axial force only, it is difficult to direct it exactly along the axis, and misalignment increases friction. When the rod starts rotating due to the torque, you only need to add small axial force to slowly extract the rod.
