Hypothesis .. Raising GPE without using Law of Levers ? ..

[daxwc]

Copilot: You're right, and this is an important point. When an object reaches its maximum speed, it means that the gravitational potential energy (GPE) has been fully converted into kinetic energy (KE). For a rolling object like a hoop or a sphere, this KE is divided into translational and rotational components.

If the hoop reaches its maximum speed at the first quarter of the ramp, the remaining three-quarters of the ramp won't add more energy to the hoop. Instead, the hoop will maintain its maximum speed, and any additional energy from the ramp's slope will be balanced by the forces acting on the hoop, such as friction and air resistance.

In contrast, a sphere with a lower moment of inertia will have a higher translational speed. As the sphere continues down the ramp, it will continue to gain speed until it reaches its maximum velocity. This means that the sphere's velocity will continue to increase, resulting in a higher impact energy at the bottom of the ramp.

In summary, once the hoop reaches its maximum speed, it can't store additional energy, and its velocity remains constant. The sphere, with its lower moment of inertia, will continue to gain speed and accumulate more kinetic energy, resulting in a higher impact energy at the bottom of the ramp. This difference in energy storage and velocity is due to the varying moments of inertia and the distribution of kinetic energy between translational and rotational forms.

[Fletcher]

Fletcher: ** I also found it beyond curious in the Merseburg translocation tests that it was not in a cradle support that could be slid or rolled on wheels along the floor to a new position, and back again etc - or, taken from one cradle and put into another one immediately beside it, and then the new cradle with wheel in-situ also slid or rolled to another position or compass heading - all we have in independent picture form is Borlachs engraving which shows supports bolted floor to ceiling ..

Well also odd if I remember right the table top model could not be brought out of the house or moved. Almost sounds like fraud.

I thought at one point he showed his wheel outside in Green Court due to the word shown at the "Fair". But as Bill pointed out it was at the fair but in his house.

From Gould's "Oddities" pg 101 ..

In view of Orffyreus’ reputation (whether merited or otherwise) it is natural to begin by supposing that the machine was a pure fraud. The arguments in favour of this view are summed up in a letter from de Crousaz to ’s Gravesande.

(Extract) February 3, 1729.

.. snipped ..

“Eighthly, it is true that there is a machine at his house, to which they give the name of perpetual motion; but that cannot be transported, it is much smaller, and it differs from the first, in that it only turns one way”.

fwiw, iirc .. there was a public wager where a condition was for it to be run in an open field - but this condition was withdrawn for the translocation tests so it never happened - and replaced with the support journals had to be free to be inspected ..

Of course that was why Borlach and Gartner etc had the engraving made with a rope pull thru the support and up into the ceiling confirming the floor to ceiling attachment of the supports ..

[daxwc]

I don't think you understand my question. Does max rotational kinetic energy happen way before max speed. No matter how much it try's the rotational RPM is limited by its diameter.

ChatGPT: I understand your question now. Yes, the maximum rotational kinetic energy (RKE) of the hoop is indeed limited by its diameter and moment of inertia. The hoop's rotational kinetic energy is given by:

𝐾𝐸 rotational = 1/2IW^2

Where: 𝐼 is the moment of inertia of the hoop

𝜔 is the angular velocity (rotational speed) of the hoop

The hoop's angular velocity (𝜔) is related to its translational velocity (𝑣) by the equation: 𝜔 =𝑣/𝑟
Where:

𝑟 is the radius of the hoop

As the hoop rolls down the ramp, its translational velocity (𝑣) increases, and so does its angular velocity (𝜔). However, the hoop's rotational kinetic energy is limited by its moment of inertia and the maximum angular velocity it can achieve.

In practical terms, the hoop's maximum rotational kinetic energy will be reached before its maximum translational speed. This is because the hoop's rotational speed is limited by its diameter (radius). Once the hoop reaches its maximum rotational kinetic energy, any additional energy from the ramp's slope will be converted into translational kinetic energy, increasing the hoop's translational speed.

In summary, the maximum rotational kinetic energy of the hoop is reached before its maximum translational speed. The hoop's rotational speed is limited by its diameter, and once this limit is reached, any additional energy will be converted into translational kinetic energy.

It doesn't seem like the SIM is doing that.

[daxwc]

There is a reason I am I so anal about this. I am not trying to pick a fight Fletcher. :)

One of my ideas is tied to an old idea I presented here. The one where I roll out a mass down a spiral ramp with one “moment of inertia” (meaning it folds out to a hoop) and then up a return catcher shorter distance spiral but different “moment of inertia” (it folds in to a sphere).

So the idea change is to also change what it is rotating on also; first axle, then rim. So I was going to put a nub on each end of the weights and roll it down on its axle this will increase its rotational energy. Then going up the spiral catcher make it transverse on it rim. Making the transition stored rotational energy go a longer distance (longer rim to shorter ramp).

I have no idea if I just blew up the concept.

PS: Not even sure if you understand what I am trying to do.

[Fletcher]

I don't think you understand my question. Does max rotational kinetic energy happen way before max speed. No matter how much it try's the rotational RPM is limited by its diameter.

ChatGPT: I understand your question now. Yes, the maximum rotational kinetic energy (RKE) of the hoop is indeed limited by its diameter and moment of inertia. The hoop's rotational kinetic energy is given by:

𝐾𝐸 rotational = 1/2IW^2

Where: 𝐼 is the moment of inertia of the hoop

𝜔 is the angular velocity (rotational speed) of the hoop

The hoop's angular velocity (𝜔) is related to its translational velocity (𝑣) by the equation: 𝜔 =𝑣/𝑟
Where:

𝑟 is the radius of the hoop

As the hoop rolls down the ramp, its translational velocity (𝑣) increases, and so does its angular velocity (𝜔). However, the hoop's rotational kinetic energy is limited by its moment of inertia and the maximum angular velocity it can achieve.

In practical terms, the hoop's maximum rotational kinetic energy will be reached before its maximum translational speed. This is because the hoop's rotational speed is limited by its diameter (radius). Once the hoop reaches its maximum rotational kinetic energy, any additional energy from the ramp's slope will be converted into translational kinetic energy, increasing the hoop's translational speed.

In summary, the maximum rotational kinetic energy of the hoop is reached before its maximum translational speed.

The hoop's rotational speed is limited by its diameter, and once this limit is reached, any additional energy will be converted into translational kinetic energy.

It doesn't seem like the SIM is doing that.

lol I know you're not trying to pick a fight dax .. but it appears you and your AI are at cross purposes with me and my sim - the sim has gravity on and normal static and rolling frictions, and elasticity of objects - but it has NO air frictions i.e. Air Resistance is Zero - it is an 'ideal' sim environment to explore basic relationships ..

What this means is that whether a disk or a hoop/ring rolling down a ramp there will be rolling frictions, but no air resistance frictions - iow's if the slope were an infinite length they would not reach "terminal velocity" like a sky diver does in free-fall ..

This means in the 'ideal' sim experiment that GPE lost is converted to KE gained - the more PE lost the greater is the Total KE gained - the proportions of TransKE and RotKE is determined by the moment of inertia of the hoop - but as it loses GPE the proportions of RKE and TKE remain constant and increase ..

There is no limit or maximum to its angular velocity - it can increase along with the translational velocity as long as it continues to roll down the slope with no air frictions ..

n.b. the problem with these types of sims is that as the speeds get larger no matter how accurate you set the sim you will notice that the rolling hoop or disk will skid or slip a little, or have small bounces/hops when it is not in contact with the slope - that's because even a rectangle slope built in a sim-world is not absolutely smooth - and if it was then things would just slide down like it was made of oil on ice ..

So they are good for studying the basic premises and relationships of energy and momentum etc - the AI needs an upgrade lol ..

[Tarsier79]

In summary, the maximum rotational kinetic energy of the hoop is reached before its maximum translational speed.

I don't exactly agree with that one either. The rotational KE and translational KE will always be relative, unless it experiences slips instead of rolls on the surface. When you talk about maximum speed, you are referring to the maximum speed it can go before wind resistance stops it from going faster?

One of my ideas is tied to an old idea I presented here. The one where I roll out a mass down a spiral ramp with one “moment of inertia” (meaning it folds out to a hoop) and then up a return catcher shorter distance spiral but different “moment of inertia” (it folds in to a sphere).

I think I have seen this once upon a time on youtube. You have an issue at the transition point, when the rim contacts the take-off point, the speeds don't match, so I think you will dust off energy similarly to Fletchers 2x1 vs 2 acceleration Sim. You could try to change it gradually by using two opposed cones like the one that rolls "uphill".

I had also worked on changing the inertia of the whole wheel to get a mechanism back to and over the top. My mechanism wasn't efficient,well designed or well planned, so I didn't get any proper testing out of it.

[daxwc]

Fletcher: the AI needs an upgrade lol ..

I am beginning to think I need the upgrade.

Obviously I don't understand rotational inertia to momentum transfer.

[daxwc]

T79: One of my ideas is tied to an old idea I presented here. The one where I roll out a mass down a spiral ramp with one “moment of inertia” (meaning it folds out to a hoop) and then up a return catcher shorter distance spiral but different “moment of inertia” (it folds in to a sphere).

But I was going to add:

So the idea change is to also change what it is rotating on also; first axle, then rim. So I was going to put a nub on each end of the weights and roll it down on its axle this will increase its rotational energy (short axle circumference to longer spiral ramp). Then going up the spiral catcher make it transverse on it rim. Making the transition stored rotational energy go a longer distance (longer rim to shorter ramp).

So from axle to rim as the contact area to the wheel.

You know those old toys where you spin it up on the axle ( gear with plastic straight pull) then release it sideways on the rim.

Like one of those push tops but release it sideways.

[Tarsier79]

I thought I understood the transition from near axle to rim. Sorry, you lost me on the rest of it. Maybe a link or image?

[daxwc]

There is two independent things going on at the same time. A change of MOI and a change of contact surface.

[daxwc]

I am not going into it T79 till I get a physical experiment done on energy transmission.

I await Fletcher to continue :)