re: energy producing experiments

[Tarsier_79]

The two 1 kg masses at 80 cm are the same rotational resistance as the two 40 kg masses at 2 cm, because they are at forty times the radial distance.

Except they are not.

[Delburt Phend]

You can put the balanced masses at any distance you want. I have not used so large a radial difference (2 cm to 80 cm) but I have confirmed the principal with experiments, with less dramatic differences.

Are you speaking from experimental knowledge; and if so, please sight the experiment.

Fundamentally what you are saying is that in takes more force to rotate the long side of a balanced tube or beam; than the force needed to rotate the short side. Please explain how that might be possible as it is a ridged object. And how were you convinced of this without experiments?

[Tarsier_79]

The inertia of a point mass in rotation is I=mr²
The two 1 kg masses at 80 cm will be much harder to accelerate than the two 40 kg masses at 2 cm.

The simple proof is the period of a pendulum. The formula is T²=L/g. Note there is also a squared relationship. The period of a pendulum is derived from its inertia and acceleration. The squared (or square root) part of the formula is from inertial math.

So when um, when you double the length of the pendulum, you see that the period increases by a factor of square root of two.

[Delburt Phend]

If your mr² is correct, then a pendulum bob of 2L would be 4 times harder to move than a bob at 1 L; clearly this is a false statement. The inertia of a bob is unchanged no matter what the length of the pendulum. The bob accelerates itself it is not under torque from the point of rotation.

The period of a pendulum has to do with the length of the swing and the sine of the angle; this is not what is being discussed.

MIT Physics Demo -- Center of Mass Trajectory

Rotation about the center of mass requires that the linear Newtonian momentum (mv) on one side is equal to the linear momentum on the other side. It is not about angular momentum conservation or energy conservation. The energy of one side is not equal to the energy of the other side and the angular momentum of one side is not equal to the angular momentum of the other side.

If a 40 kg mass is attached by a long tube to a one kilogram mass on the other end, and it is flipped in the air, it will rotate about its center of mass.  And 40 kg * r = 1 kg * 40 r. 

Explanation of the universe must correspond with what the universe does. And the universe does Laws of Levers and the linear momentum (mv) of one side is equal to the linear Newtonian momentum of the other side.

Do the experiments what do the experiments tell you; this is only worth about 10 trillion dollars.

[Tarsier_79]

If your mr² is correct, then a pendulum bob of 2L would be 4 times harder to move than a bob at 1 L; clearly this is a false statement.

It is 4 x harder to move.

The inertia of a bob is unchanged no matter what the length of the pendulum. The bob accelerates itself it is not under torque from the point of rotation.

The reason the pendulum length is not a linear relationship to the period is the same reason inertia doesn't have a linear relationship with mass/radius. A pendulum is the same as your lever. Instead of looking with tunnel vision at the problem, consider the similarities. Gravity provides a constant acceleration F=MA
If I double the length of a pendulum/lever-weight, Gravity doubles the torque on the system (leverage), but it doesn't take the same time to rotate. (because it is squared)

The period of a pendulum has to do with the length of the swing and the sine of the angle; this is not what is being discussed.

That is the funny thing with Energy math. Everything relates to each-other, as it should.

The period of a pendulum, gravity accelerates a mass around a pivot point. Your see-saw 2 masses are being accelerated around a pivot point. Regardless of where you apply torque: to the center of rotation, or the furthest mass from the center, the inertia increases exponentially.