just for the record:
Torque is rotational kinetic energy....use it or lose it.
Angular momentum is result of applied torque over a period of time.
We're going to solve for angular momentum, mostly because it's easier to understand. Think of a baseball player swinging a baseball bat. There is angular momentum along the entire bat. The farther out the ball is when it's hit by the bat, the more force, the farther it flies. Easy to observe and understand.
(We're going to treat the wrist thing in the following experiments as irrelevant, since you would be moving your arm as well. To simplify, we'll say that, like a newbie would, you swing your khukuri with a stiff wrist (no snap) and you start straight above your head and swing down to waist level. )
Experiment #1
So, assume the following:
2 objects
#1 is 20 inches long
#2 is 25 inches long
Equal Mass (same weight on earth)
Equal angular velocity (swung at the same speed)
The test person's "reach" is 25 inches. (reach = distance from point of rotation - shoulder - to the center of palm - where you'd grip a khukuri)
Radius #1 = 45 inches (1.14m for science folks)
Radius #2 = 50 inches (1.27m)
The equation for determining Angular Momentum is:
L = M V R = Mass * Angular Velocity * Radius
If M#1 = M#2 and if V#1 = V#2
(see assumptions above)
Then the ratio L2 : L1 can also be written R2 : R1
They are directly proportional.
Additionally, the torque is being applied at the point of rotation - again, oversimplified...but it's like saying we're comparing apples to apples....in other words, I'm assuming your swing/form will be similar between the two khukuris.
Experiment #2
Now, we look at it a different way.
Mass not Equal (we'll use a 1:1.25 ratio)
Angular Momentum held constant
Velocity held constant
L1 = L2
That would mean:
M1*V1*R1 = M2*V2*R2
(1)*V1*(1.14) = (1.25)*V2*(1.27)
Solve for the ratio of V1:V2
V1/V2 = [(1.25)*(1.27)]/(1.14) = 1.39
V1 = 1.39*V2
So a 20" would require 1.39 times the speed in order to equal the angular momentum created by a 25" of 1.25 times mass.
Kinda makes sense, don't it?
Experiment 3
(similar to 2)
As observed by me while testing the 22" GRS (#1) against a 20" AK (#2) of nearly equal mass.
Equal Mass
L=MVR
L1 = L2
M1*V1*R1 = M2*V2*R2
cancel out Mass numbers since M1 = M2
V1*R1 = V2*R2
V1*(1.19) = V2*(1.14)
V1 = 0.96*V2
V2 > V1
In other words, I would need to swing with less speed with the 22" GRS to achieve the same angular momentum.
Additionally, since Torque = Radius * Force
If I apply the same torque.....
T1 = T2
R1*F1 = R2*F2
1.19*F1 = 1.14*F2
F1 = 0.96 F2
...less force is needed to move the 22" khukuri.
This, at first seems counterintuitive....and please feel free to check the numbers.
But it's based on a few "givens"....
First, we're comparing khukuris of equal weight.
Second, we're applying the same torque, in order to generate the same angular momentum.
If you take a heavier/longer khukuri and swing it at the same speed as a short one, then yes, it will take more energy. But then that would fail our two assumptions.
A test that would get you equal results would be two khukuris that were each proportionately equivalent...that is, fit the ratio we like to use here in the forum of being 1.5 ounces per inch.
My test above was apples and apples. This test would be oranges and oranges.....just can't cross the two without serious complications....
)
