### The Physics of a Blocking a Kick By: Nestor Komar

During a recent Karate exercise, we were required to block a snapping sidekick. I was intrigued with a fact that is well known to all of us: that is that as we cut down the distance between ourselves and the kicker, the impact felt by the blocker is lessened considerably. As a mathematics prof, I was immediately reminded of a formula for linear velocity as it relates to angular velocity. I shall try to explain, as simply as possible, the relationship between the two.

Angular velocity is simply the speed that a rigid object takes on as it rotates about a fixed point. In Karate, assume that the leg (rigid object) rotates from the hip (the fixed point). The formula for angular velocity (called ) is defined as follows:

a = 0 / t

where "0" represents the angle of rotation and t represents the time taken to rotate through that angle. Thus, the units for angular velocity could be in degrees per minute or rotations per minute or, more appropriately for the kicker, in degrees per second! The angular velocity has a direct relationship with the angle of rotation; if the kick is allowed to accelerate through a greater rotation, it will hurt more. If the blocker anticipates and can side step into the kicker's path, the angular speed of the leg can be reduced (read as the sting of the kick is lessened considerably).

Linear velocity, (as it relates to its angular velocity counterpart), is the speed at any point on the rotating body and is proportional to the radial distance from the center to that point. To illustrate this fundamental truth, think of a record turning on a record player. A penny has to travel a greater distance in the same amount of time if placed on the rim of the record as opposed to the same penny placed in the centre of the record. The same principle is at work in playing crack the whip. If you are near the centre of the whip you have little to fear from a rotation but if you are at the end of the whip you are moving at a fairly good clip.

The formula for linear velocity looks like this:

v = a x r

where "a" is the angular velocity as before.

So what's the point? If you decrease the distance r between the attacking, rotating leg the speed with which it hits you is reduced. Cut the distance and cut the pain.

Let's put these ideas together now. If we move in the direction of the attacker's hip (pivot point), we cut down the leg's speed. By moving into the rotating leg, we cut down the angle of displacement. This also cuts down the leg's speed. By moving in and into the path of the leg, we decrease the angle of displacement and the radial distance, thus we can considerably reduce the speed that the leg can hit us with. We all know from experience that a slower leg doesn't hurt as much as a leg that has speed behind it.

Ain't science grand?

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