Why does twisting a cork make it easier to remove from a bottle? When we want to remove a cork from a bottle first we turn the cork. Turning in one direction makes it easier to remove in the axial direction.
Does anyone know something more about this?
 A: Interesting question. Here is how I would explain it -
It is important to note that it is NOT a necessity to pull while twisting the cork, if you have appropriate openers that use leverage, then its probably the best and easiest way to go about it.
So this question can only be answered in the context of NOT having appropriate tools. To be precise in the answer let select such a tool, the most common way is to use a flat small knife and pierce into the cork then pull it slowly while rotating it.
Breaking this problem in all the working components, we have,

*

*The knife that's used as an opener

*the cork

*Human muscle, which provides the essential force

*The bottle neck in contact with the cork

So WHY DOES ROTATING WHILE PULLING MAKES LIFE EASIER?

*

*In the context of the tool you use -

As already mentioned, unlike bottle caps (that has thread on it) rotating a cork to open it is not a necessity. But whether you want to rotate it highly depends on the tool you use. In our case we are using a knife. Now you can pretty well see what's gonna happen if I just pull it. The knife will come out just as the way it went in, meaning there is no hook or grip on the knife, other than friction between knife surface and cork, to hold the cork while its being pulled out. So the only way is to slowly pull the system using a rotatory motion.
What does rotation generate?
Among other things that is discussed below, it generates a higher pressure between the knife surface and the cork (you are essentially pressing the knife surface hard against the cork), hence INCREASING THE FRICTION. Now that we have increased friction, we can use more force than that would have been possible if we weren't rotating.


*The cork -

The cork is freshly cut (meaning its very likely being used for the first time), hence the surface is usually very rough. In fact this is essentially the reason why you cant use a cork multiple times without leakage. When you rotate, you are essentially doing the job of what a stone grinder would do. You are grinding and polishing the surface of the cork in contact with the bottle. Now, its a known fact that, smooth surfaces move around easily as compared to rough surfaces (this is essentially the reason why vehicle tyres have various pattern on it and not bald).


*The Physiological side of it-

You are applying force using human hands, and any discussion regarding the same would be incomplete without considering them.
It can easily be verified that rotating the wrist is very different from pulling your arm closer to you, meaning the muscles involved are different in both the context (Check it out yourself by trying to rotate the wrist and then pulling something all the while feeling which muscles are tense)
Since we are using different muscles in combination, it is natural to feel more easier to rotate and pull vs just pull.


*Bottle neck -

Notice the the bottle neck is almost always more wider on the outside than the inside (and so corks also have the same shape). This essentially helps in redirecting the normal force due to the cork in slightly outward direction (reaction is perpendicular to the surface and the surface here is included). Hence in a vague sense, you are essentially using the rotational motion to generate an upward force, contrary to the usual situation where everything (torque, motion, etc) in a rotational motion is perpendicular to the axial motion.

Point 4 can also be applied to say that rotational motion essentially changes static friction (due to chemical bonding as explained in another answer by @annav) to kinetic friction, which remains kinetic in the axial direction despite no motion along the axis (elaborating the answer by @steeven).
A: Its all angles and body geometry.
So obviously the cork can be pulled straight out.  That's what corkscrews do.  So we know the cork can handle the stress of being pulled out, or rotated.  It must be in the hands.
If you pull the cork out, think of what muscles you are using.  You have to use your shoulder and upper arm muscles.  Look at the leverage you have.  Not much.  Contrast that with rotating the cork.  If you rotate the cork, its a rotation about a very small axis, and your body is designed to be able to clamp down and direct all of its muscular force into generating that torque.  Just estimating, a cork is about 12mm in radius, and the human arm is around 600mm, so you have around a 60x mechanical advantage when turning.
Once its turning, this gets to Steeven's answer.  The turning means we no longer deal with the static friction of the cork against the glass.  We only deal with its kinetic friction.  This is typically much lower, so now it is much easier to use those big muscles axially.
A: tl;dr–  Twisting the inside of a cork can compress it, making it easier to remove.  The same method is used with foam earplugs.

Twisting makes the cork smaller.
Materials tend to get compressed when twisted internally.
Examples:

*

*Foam earplugs.Foam earplugs are basically the same thing as corks, in that they're stoppers made of somewhat-compressible material.  To insert such earplugs, people roll them into a tighter configuration, which compresses them.  Then they can go into an ear.


*Fork in spaghetti.To eat spaghetti, folks will often insert a fork and twist the fork around.  This causes the spaghetti to tighten around the fork, making it easier to pick up.


*Drying fabric.Say a towel or other fabric is wet.  Then, someone might twist the material tight to compress it, forcing out the water inside.


*Threading a needle.Needles have little holes on them for thread to go through.  But frayed thread can be a bit too big to get in; so, someone might twist the thread to compact it, making it much easier to thread a needle.
So, if someone twists a cork, it may help compress it.
A: When the cork is stuck and stationary, it is static friction which is culpable in keeping it fixed.
As soon as the cork moves - in any direction - the static friction is replaced by kinetic friction.
Kinetic friction, $f_k=\mu_k n$, is typically lower than the maximum static friction, $f_s\leq \mu_s n$ (because the kinetic friction coefficient typically is smaller than the static friction coefficient, $\mu_k<\mu_s$), and so, whenever you want to move something that is stuck, try to make it twist and turn and move before pulling it out.

With some downvoters and commentators bringing to my attention, that the answer above is not fully sufficient, I have below added the missing half covering the question of leverage.
Naturally, it is only a good trick to rotate the cork and then pull it out, if overcoming static friction to make it rotate is easier than overcoming static friction by pulling it straight out. As the comments mention, this can indeed be easier due to leverage:

*

*Pulling it straight out requires the force, $F_{pull}$, exerted by your arm to match and overcome that of the static friction, $f_s$, fully, one-to-one. You are then fighting Newton's 1st law directly and must exert a force:
$$\sum F > 0\quad\Leftrightarrow\quad F_{you}-f_s>0 \quad\Leftrightarrow\quad F_{pull}>f_s$$
There might other contributing factors to the necessary force as well, such as the pressure in the bottle as another answer points at.


*Rotating the cork can be done by applying force at the far ends of the handle of the cork screw/wine opener tool. That force creates a torque, $\tau$, and the farther away, $r$, from the centre the force is applied (the greater the leverage), the greater does the torque become:
$$\tau=F_{you}r_{handle}.$$
This torque in turn causes a shear force, $F_{cork}$, against the static friction forces at the cork perifery. As long as the tool handle allows for more leverage than the radius of the cork itself, $r_{handle}>r_{cork}$, then you can with less force at the handle generate enough force at the cork perifery:
$$\tau=F_{you}r_{handle}\quad\text{ and }\quad \tau=F_{cork}r_{cork}\quad\Leftrightarrow\\
F_{you}r_{handle}=F_{cork}r_{cork}\quad\Leftrightarrow\quad F_{you}=F_{cork}\frac{r_{cork}}{r_{handle}}.$$
Since it is now this new force, $F_{cork}$, that must overcome static friction, $F_{cork}>f_s$, and not your own pulling force, and since the twisting force, $F_{you}$, you apply is smaller than, $F_{you}<F_{cork}$, then it is much easier to make the cork rotate and thereby overcome static friction, and then apply a subsequent pulling force that easier overcomes the smaller kinetic friction.

A: As Steeven said, kinetic friction is a smaller force than static friction. Once the cork is moving in any direction, it is easier to move in the direction you want.
As Anna V said, bonds may be broken that make it easier to move a second time after it has moved once.
So why is rotation easier than longitudinal movement? Think of a screwdriver. A large diameter handle allows you to exert a large torque on the screw. That is, small forces a large distance from the axis apply large forces a small distance away. So the large handle on the corkscrew helps.
A: Let me take a shot:
The cork has made chemical bonds with the glass. These are the same for all dS of the cork surface: the difference is that in rotating the cork because of the circular motion, a small d(theta) brings the surface unstuck, the resistive forces will not add( different directions). For the axial direction the surface is continuous and the forces needed are additive. Once it becomes unstuck then axial force is effective, because it takes time for the bonds to form, between cork and bottle.
A: The initial twisting step is just ergonomically easier than the initial pull it would be require to get the cork moving. For this you have to overcome the static friction between cork and glass. Also there may be van der Waals forces that need to be broken before the cork starts moving. Once the cork moves the friction is lower and it can be pulled. Note that mechanical devices don not bother to twist, they just pull.
A: 
Why does twisting a cork make it easier to remove from a bottle?

When you apply an axial force and, possibly, a torque to the cork (and, opposite, to the bottle), you generate a state of tangential stress between the cork and the bottle neck.
With $A$ being the area of contact, $N$ the axial force and $W$ the torque, the longitudinal component is $\tau_{rz}=N/A$ and the tangential component is $\tau_{r\phi}=W/(rA)$, $r$ being the inner radius of the neck.
Because the cork begins to move when the resultant of the tangential stress between the cork and the bottle's neck
$$
\tau=\sqrt{\tau_{rz}^2+\tau_{r\phi}^2}
\tag{1}
$$
exceeds the friction bond, you can recognize that applying a torque  (twisting the cork) reduces the axial force $N$ that you need to exert.
After establishing that applying a torque reduces the $N$ needed to start moving the cork, when the cork starts moving it's all down hill because the friction coefficient is different (static vs dynamic friction) and also the surface of contact is continuously reduced.
