Momentum

Momentum is important when considering the force of a strike, or just how much energy an object has when it is in motion. Newton's First Law states:

In space, far away from the gravity of the Earth, the Sun, or any other stars, if you throw a ball out of the airlock of a spaceship, it will continue in the same direction and speed forever. This is because no other force is applied to it (Yes, I realize that gravity is virtually inescapable on a galactic scale, so consider this just a thought experiment). In martial arts, we hardly think about it, but when you smash your fist into a punching bag, you had to accelerate your hand toward the target, and the bag was very content to stay at rest until you hit it.

When an object is in motion, it has a certain amount of energy. This is kinetic energy. In general, this is the relative motion between two objects, as there is no way to measure intrinsic speed without somehow comparing it to another object. The equation for momentum is:

Equation 2:

p = momentum, m = mass, v = velocity

This shows that momentum is defined as the mass of an object times the velocity of an object. Since momentum is the product of mass and velocity, it is directly proportional to both. A single object, such as a martial artist's fist, can have different momentum depending on its velocity. For instance, when a martial artist punches, the mass of her hand stays constant. What matters is the velocity. The higher the velocity, the greater the momentum. To a martial artist, momentum is power! A martial artist must accelerate to get speed, but high acceleration doesn't mean something is going fast. Even with a high acceleration, at time 0.0, the velocity is still nothing.

To see why this is important, we will consider a punch with 15 m/s² acceleration. The mass of the fist is 3 kg. This means that the martial artist has to generate 45 kg m/s², or 45 N, to throw the strike.

Using f = ma:

However, at time 0.0, when the martial artist is just starting the punch, the momentum is 0. Thus, even though the martial artist is generating 45 N from the start of the punch to the end, it does not have any striking power until the punch is moving. It doesn't become a strike until after some time t > 0, because its momentum is small.

This is why stopping a kick or punch when it just starts is a lot easier then when it is going fast. However, even if you stop it at time 0, you will still feel the force being generated by the arm or leg.

Figure 2: Momentum

In Figure 2, there are three constants; force, mass, and acceleration. Assuming she puts the same amount of effort into the punch, so her force is constant, over a short time the other variables remain constants. As time increases, so does momentum. The longer an object accelerates, the faster is it. The ion drive space propulsion technology works by using this principle. Unlike rockets, which supply maximum power over a short time, the ion drive applies a small but constant force. Eventually, given time, this can lead to great speed. Whenever performing a technique that requires lots of power, you should try to maximize acceleration time, because this maximizes momentum. If you throw lots of strikes, then you know that short-range punches have less power, even if you put your maximum effort into it. You can fix that by accelerating longer.

Now that you are familiar with force and momentum, we will go over some stuff you can do with it. Forces are our main weapons. Forget fists and feet, as they are merely ways of delivering some Newtons (a measure of force) to an opponent.