Hello Harry. Let's make sure I'm on the same page with you on this pendulum matter.
Are you claiming the pendulum arm is going to swing back-and-forth with the exact same periodicity frequency regardless of whether the spin-bob wheel has the breaks on or off? > Steven wrote: > <snip> >> In any case I can see how it's very tempting to believe >> that the pendulum arm's periodicity will not be affected >> regardless of whether the break is applied or not applied, >> but unfortunately that's not the case. I had, in fact, >> toyed with this possibility myself for a brief period of >> time, until Mr. Lawrence correctly showed the flaw in my >> reasoning. The pendulum arm's periodicity WILL definitely >> be affected depending on the application of the break to >> the spin-bob wheel. When the break is ON, the length of >> pendulum arm is effectively longer causi > This is inconsistent with the theorem. > The length of the "arm" is the distance from the centre of > mass of the bob to the pivot point. The Theorem says it is > THIS distance which governs the period.The radius of the > bob and the state of the brakes do not change this distance, > so they do not affect the period. I believe this is where the problem (or inconsistency) lies. I believe you are selectively reinterpreting portions of the theorem to suit your diagram particularly in regards to when the break is applied. Unfortunately when the breaks are applied this DOES effectively change the pendulum arm's distance, and as such, the periodicity of the pendulum swing. When the break is applied to the spin-bob wheel you must add its inertial mass to the inertial mass of the pendulum arm. By the sacred laws of Newtonian physics this must slow things down a bit, or else the physics books will have to be rewritten - followed cats and dogs soon living together. This is why I have consistently suggested re-envisioning your diagram with the spin-bob wheel three times the size of the pendulum arm as this should make the change in periodicity more obvious depending on whether the breaks are applied and when not applied. >> This is precisely why this apparatus does not make >> additional energy. >> >> Again, I recommend increasing the size of the spin-bob >> wheel to around three times the length of the pendulum arm. >> Hopefully, this will make the experiment more easy to grasp >> as the ramifications of the theorem you state, specifically >> the changes in periodicity due to changes in length, should >> be more obvious visually. > As I said above, the parameter that counts is the distance > from the pivot point to the centre of mass of the bob. Indeed that is the case when the breaks are not applied - pendulum arm swings faster. And that is NOT the case when the breaks are applied - pendulum arm swings slower. I suggest another visual exercise particularly since you are very good with Adobe Illustrator. Create two distinct diagrams where both models possess the exact overall 3-D dimensions and mass distribution. (1) The first model contains two distinct parts that move independently of each other, a pendulum arm and a spin-bob wheel where they are attached through a frictionless bearing. IOW, the spin-bob wheel spins freely and independently of the pendulum arm's swing. (2) Next create another model with the exact same dimension of the first model but where the pendulum arm and the so-called spin-bob wheel are actually physically attached together as one solid unit. As previously stated, it's imperative that both models possess the exact same mass proportioned in the exact same locations. Now, swing back-and-forth both devices, in your head. What do you think the periodicity is going to be for both models? The same or different? Regards, Steven Vincent Johnson www.OrionWorks.com
