Creating power relies on speed created as much as it does on mass moved. Even though the mass is so insignificant, the massive amount of speed and torque that the arm experiences, along with the high speeds of the projection of the ball out of the hand (remember that radar guns measure the speed as it crosses the plate; a pitch will deccelerate by about 1mph for every seven feet traveled; a 100mph fastball has a "muzzle velocity" of 107) are so much higher than any speed created during sprinting or heavy weightlifting or anything like that. The arm moves 7000 degrees/second.
Even though the arm isn't moving a heavy weight, to approach the same type of power, a weightlifter would have to move thousands of pounds at a significant speed. The torque applied to the arm is insane as well.
Take the squat for example. If you use the knee joint as the place to measure degrees of movement, then a 1,000 lb. squat would have to move at less than 1/7 the speed of the pitching arm to equal the same power produced.
Basically, the body (or the bar) would have to travel from the bottom of a squat at just under 1/7 of the speed that the pitching arm moves at to create more power, if we assume that power=mass x speed.
I see what you're saying. Power is defined at work/time.
These two examples below should equal the same about of work, right?
Can we assume that we have about 10lbs moving at 110mph?
Would that then equal 200lbs moving at 5.5mph?
How long does it take for a pitcher to accelerate his arm up to speed? 1/5 of a second?
I wish there was some way to measure it. But it's really hard when you're dealing with such short durations, that's why in my original post I mentioned at least 1 second.
I think you are right though, the power output of a fast pitch is very high. It's just hard to imagine since it doesn't primarily use the large muscle groups.
I believe that in any "explosive" or "powerful" movement, there is some sort of pivot point or axis upon which degrees of movement can be measured. The movements that have a high amount of degrees per second will have the highest speeds generated. This kind of makes the speed of anything being projected from the body immaterial since the speed of those objects are affected by many other factors besides the power generated to move them (air resistance, gravity, drag, etc, etc.)
The pitching movement actually does use the large muscle groups to generate the power. The midsection and thighs uses momentum and torque to allow the arm to experience what would otherwise be extremely traumatic over and over again. That is why any pitching drill that does not incorporate the legs creates an arm motion that is actually completely alien to the arm motion needed to throw at high speeds with an acceptable amount of stress on the elbow and shoulder.
As for one second, remember that most of the truly explosive, powerful movements take much less than a second to occur. Even sprinting, which seems very powerful, isn't nearly as explosive as a hammer throw. The sprinter is generating a lot of power in trying to move an object close to or more than 200lbs, but he really isn't going fast at all until he hits top speed, which is probably only about 28mph anyways.