The Paradox Engine

[broli]

broil,
I like the bullet experiment!
The explanation that was given is obviously not correct or the results would have been significant enough to be seen.
How can the rotational energy be 50% of the gravitational energy and yet the penetration difference is immeasurable.

What doesn't make sense about this problem?

You got stuck on a none issue. That experiment is not guess work, it's a tried and true fact of common day physics backed up by countless experiments.

At no point did anyone say the final energy was more than the initial energy. In a ballistic pendulum experiment you can loose as much as 99.99% of the initial energy while you will conserve 100% of the linear momentum. The Linear momentum of a rigid is always conserved irregardless whether the impact was offset to the center of mass. Sure you end up with more conserved energy which is seen as rotational energy, but still not as much as your initial energy.

[lumen]

You got stuck on a none issue. That experiment is not guess work, it's a tried and true fact of common day physics backed up by countless experiments.

At no point did anyone say the final energy was more than the initial energy. In a ballistic pendulum experiment you can loose as much as 99.99% of the initial energy while you will conserve 100% of the linear momentum. The Linear momentum of a rigid is always conserved irregardless whether the impact was offset to the center of mass. Sure you end up with more conserved energy which is seen as rotational energy, but still not as much as your initial energy.

Another interesting viewpoint is extracting the conserved energy from the blocks.
The non rotating block lands on a bar directly contacting the center of the block. At this point the most possible gravitational energy is extracted.

The rotating block must land on a bar at the same offset as the bullet strike (other side) to counter the rotation in order to conserve the same energy as the non rotating block landing on the center point. (bullet strike point)

If the rotation conserved additional energy, why would more energy not be extracted from the rotating block?
If the rotating block landed on the center of the block, less energy would be extracted.

The problem does not seem to be fully accounted for.

[Tusk]

That's quite a torrent of free thinking infringer  I'll basically let you get on with it until the dust settles for you, but this comment:

I think what we may need is a bit more simplified terms for people.

..... I'll attempt to go down that road a little further but I've discovered that this can lead to picking through the discarded minutia and throwing it back as proof of error.

I was actually expecting a slight deviation in the vertical plane of the axle for the arm,, so that when looked at straight down it was making a small circle and that this deviation would be close to 90 degrees from the arm position while under acceleration.

I think I see what you're looking for webby1; a reaction for the applied force in the body of the apparatus? If so then I'll just pop a sketch of my original concept, where I was hoping for an inertial drive system (image attached at end of post). Btw it didn't move either, but it did get me thinking

and lumen:

If the particle's energy was completely absorbed into the bat in each case then why would you consider that the case with rotation contained any more energy?

Because in the period of the collision, the bat moves further at the end than it does with the collision at the centre of mass, which in turn causes the point of force motion to be greater ergo more energy. The simple statement 'having the same force applied' is heavily loaded; applying the same force to say, a bowling ball and a golf ball, first and foremost the period of application of force must be equal else the experiment has no meaning. So over the period of application of force, the bowling ball moves a few inches and the golf ball a few feet (let's allow, at least). So the point of application of force has advanced significantly further for the golf ball, which requires additional energy, which in turn explains why the golf ball exhibits a more energetic motion than the heavy bowling ball. In our case the rotation follows similar lines.

Also if you take a look at the image I attached for webby1, there is no motion of the apparatus despite there being a pair of reactions at the drive units attempting to impart motion to the body of the apparatus. The only possible conclusion is the one I have provided; the secondary reactive forces at the axis of the disks exactly cancel these two primary reactions. Otherwise there would be a breach of CoM (which is initially what I was hoping for btw).

I had this aspect sorted and defined long before the M.I.T. paper was discovered, and until that time very few seemed to believe my findings. This is no longer in contention, rather the interaction between the two phenomena seems to be the current stumbling block. There is no doubt that the three linear motions of the baseball bat in the M.I.T. example are equal; and since the motion of rotation must produce greater energy than non rotation, therefore the rotating bat must have had more energy imparted to it, and must also have more energy to yield.

[Tusk]

Sounds like you have a mind for 'out of the box' thinking webby1. Presumably you didn't defeat CoM with your designs, or is my faith in that fundamental phenomenon misplaced? That might be my only concern regarding the PE concept, since it depends on CoM to function

This for broli:

I had another quick glance over your replies and I may have an answer to your obvious discomfort with the 'extra energy' issue. I'm attaching a graphic below which represents a disk (A), if we can allow that it is mounted on some sort of cart (thus constituting an 'assembly') perhaps with rails to run on; and there is also a 'brake rail' (B) running parallel to the rails. The disk is already rotating at the start of the experiment.

We know that if the brake rail applies a retarding force to the disk a reaction manifests at the point of force on the brake rail; a secondary reaction manifests at the disk axis as shown; and of course the disk rotation is retarded. This arrangement is really quite similar to that already discussed, but with the disk already rotating with X kinetic energy. Finally we can allow that the linear motion of the disk (due to the secondary reaction at the axis) manifests such that all rotation ceases as the disk passes point C on the brake rail. Linear acceleration will also cease at point C, but the disk assembly now has Y kinetic energy.

Note that I have named the applied force and the primary reaction based on the perspective that the brake rail applies force to the disk, mainly to highlight the similarity between this example and those considered previously, and account for the linear motion with more clarity.

If we now allow that a length of steel was in linear motion at velocity V with X KE; we then reform the rod into a circle, mount it as in the example on a weightless disk assembly in a frictionless environment and specify a theoretical 100% efficient brake system (i.e. no heat, sound etc).

Then we rotate the disk such that any point on the reformed rod has circular velocity V, so that it's KE will again be X.

At the end of the experiment the linear velocity of the disk assembly will again be V and therefore the KE will be X (ergo for these conditions Y = X ).

Before proceeding further with this example I will pause for comment, since without your allowance of the above our next point would likely be rejected.

[broli]

Tusk, that's perhaps an easier setup to analyze. However I would like to state that the rotating version is not the same. If you would compare them, for instance accelerating both rod and wheel at the same rate, in the rotating version a rotation of the wheel would arise due to its inertia. While no such "spontaneous" rotation appears in the linear version.

I also performed a simple analysis of the linear setup. it does show an energy gain, but I'm looking forward to some critique pointing out the mistake in the math.