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Posted By: Andrew PalfreymanYou've made an error. Please stay late after class.Fantastic! Oh that IS good news! Thank you so much, i was starting to get into quite the fizz there! Phew!
Posted By: VibratorSo, what have i muffed up this time?
Posted By: AngusOh goodie!!! Meat and potatoes for the 'trap at last!!Quite so.
ETA It is wrong to say that the device switches instantly between its two different conditions of angular momentum without work being done.
Posted By: AngusHere's how I think about it.
You can reach the state where the weights all lie along a radius as the central wheel rotates, in two stages. Start with the weights lined up on a horizontal line.
First you let the axles on the circumference of the central wheel be free and you spin up the central wheel. The weights on the two outer wheels continue to lie on horizontal diameters of their wheels because no torque is applied around the outer axles. The angular momentum is (4 m) omega R.
Now to get the weights lined up on a single rotating diameter you have to spin up the outer wheels to the same rate. This gives you the same situation as the tidal locking of the moon. The rotation period of the outer wheels equals their orbital period. It adds another (4m) omega R to the budget. If you wind in the weights as you propose you have to do enough work to kill this momentum. Energy and momentum are conserved.
ETA I suppose the confusing issue that might lead you astray is that when the system is "tidally locked" the axles of the outer wheels do not turn in their bearings. That might lead you to think the wheels they carry are not rotating. But they are.Mate - it's the maths that are 'astray' if something's wrong. Please, i'm not claiming anything the momentum and KE figures aren't..? It's all there with its guts out, no secrets or obscure formulas..
Posted By: VibratorCheck Google if you don't believe it - MoI is given by mass times radius squared (mr²), AM is MoI times angular velocity (Iw) and rotKE is ½Iw². These are the ordinary, bog-standard terms - the most basic basics..... he said ... to the Physics Professor. Ah, well, another perfectly good cup of coffee lost.
Posted By: DuracellOh well i have come to the right place, then.Posted By: Vibrator[span style=color: red]Check Google if you don't believe it[/span][span][/span]- MoI is given by mass times radius squared (mr²), AM is MoI times angular velocity (Iw) and rotKE is ½Iw². These are the ordinary, bog-standard terms - the most basic basics..... he said ... to the Physics Professor. Ah, well, another perfectly good cup of coffee lost.
Posted By: VibratorYou know that part of Angus his reply that you quoted above to which you replied: “LOL right, not sure what you’re on about here”?Posted By: DuracellOh well ihavecome to the right place, then.Posted By: VibratorCheck Google if you don't believe it- MoI is given by mass times radius squared (mr²), AM is MoI times angular velocity (Iw) and rotKE is ½Iw². These are the ordinary, bog-standard terms - the most basic basics..... he said ... to the Physics Professor. Ah, well, another perfectly good cup of coffee lost.
Then again, we're talking basics - foundational stuff, that no one should ever forget, but which presumably doesn't get used much after grade school.. But no, you're right - this should be bread & butter to a physics prof..