As I've stated before, pivoting for certain kicks (round kick and side kick, in particular) is essential for proper execution. Even after 5 years of Taekwondo, I found that I had to make some adjustments when I moved to a dojo that required shoes. The extra friction was causing my foot to stick to the ground, preventing me from getting a good pivot. This is an experience that I've seen happen to many students. So, I'm going to explain a little trick, based in physics, to mitigate this problem.
As we all know (or should know by now), friction is the force that resists motion. That includes spinning on your foot. The formula for friction is f = mN, where m is the coefficient of friction between the two surfaces and N is the normal force exerted by the ground as the reaction force against the weight of the object (in this case, you). So, when the surfaces change the friction also changes. This is what happens when you go from being barefoot on a canvas mat to using rubber soled wrestling shoes on a vinyl mat, for example. There's not much that you can do about the surfaces involved other than choose different footwear. The thing you can control however is the normal force.
The normal force is equivalent to the amount of weight pushing on the ground at the time. This is where the trick comes in. If you take some of your weight off of the ground, then you can reduce the normal force and, therefore, reduce the friction you experience when you try to pivot.
So how do you take your weight off of the ground without turning every round kick into a cinematic flying kick? The trick is to bend your knee quickly and briefly so that your weight actually falls, momentarily, toward the ground. If you're not using the ground very much to hold you up, then it can't push back with a very big normal force, which reduces the friction. In practice, I almost think of it as pulling my heal up towards my body without an accompanying upward jump. As my foot pulls away from the ground, the friction is reduced. Keep in mind, this is only for a fraction of a second...just long enough to finish the pivot, which should be fast anyway. Here are some visual aids.
|Here I'm set, ready to kick|
|The black pants and angle make this a bit difficult to see, but|
my heal is off of the ground and my knee is bent as I pull my
heal up away from the ground a tiny bit
|Once the pivot is done, I allow the heal to return to the ground|
If a picture is worth a thousand words, then a moving picture is worth...many thousands of words. Check it out.
This particular trick is useful when performing a round kick or side kick when the ground and your shoes have a high friction coefficient. This general idea of reducing the contact force to reduce the friction has all sorts of applications elsewhere in fighting, but that's for another time. Happy kicking.