Will Friction on a cylinder embedded into the earth differ if the method of removal is changed Would it make a difference if a cylinder embedded into the ground is
1)pulled vertically or,
2) removed by rotating with the same force
 A: I think this is an interesting question. Our intuition with pulling objects out of the ground is that twisting, or rocking back and forth works better than just pulling straight out.
Some things to think about:

*

*Static friction is usually higher than dynamic or kinetic friction.

*The friction force is proportional to the area and the normal force. How you work out the normal force would depend on the situation.

*Is the cylinder open or closed at the end. If closed there is probably a suction force as a vacuum is formed, depending on how well the seal is formed. Wet or moist earth would have a better seal than say dry sand. If the earth is sticking to the cylinder you also would not be pulling just the cylinder but the mud or earth with it and that would change the problem. If the soil was more granular, or if the soils was more like a liquid and viscous would change the problem.

*We can choose to apply a force pulling the rod directly up, or apply the force radially. The torque being force times the distance from the center of the cylinder. So it is relatively easy to get a larger torque by applying the force further from the center.

*A long thin cylinder would be different than a short fat cylinder when it comes to the suction forces.  It would also change the moment of inertia.

So practically speaking, since the area in contact with the earth and presumably the normal forces are the same in both cases. The static friction would be the same, but for a long thin cylinder when you try to rotate, you are not creating a suction force at the base of the cylinder. You may also be able to have a higher torque by the way you apply the force. By breaking the static friction, and rotating first it would be easier to start to pull the rod up since the dynamic friction is less.  Even better,  if a path is created that allow the suction forces to be reduced by equalizing the pressure.
