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Re: How would I go about....
Re: How would I go about.... -- cm	Post Reply	Top of thread	Forum

Posted by: randykimball ® 04/01/2007, 17:28:42 Author Profile eMail author Edit

You said, "NO other external forces". Of course you are right, you set up, ....huge grin.....but took the bait. ... allow me this moment of fun. .... stay with me for a moment... I just want to illustrate an important engineering point... OK? With No external forces the wheel would never stop but eventually end up staying extremely close to having the weight at 180° from the top. Too close to measure, so in realistic perspective it went to 180° from the top. It would also rotate to somewhere near a certain number of degrees to a point we can get with math. However there is no case where no other external forces exist, just as in real life the wheel will never reach 180° straight down because of friction, nor will it osolate for infinity. Nor can math ever actually tell us where the weight will rotate to within the same accuracy of the size of those ifinite oscillations because of the lack of ability to know the real world friction in the those actual bearings and the actual balance of the real wheel close enough with out deviations. What I'm trying to express and stur in our minds is not a challange to calculations but a "reminder to remember" to stay realistic with design calculations (not pointed at any one person but to the general public). There is a math world and there is a real world. We can only reach the real world within a value of deviation. I was once told that a lathe operator did not need tolerances and should be able to get the product exactly right. Well, no the operator can not. The actual size of the part can only be reached within a value of deviation at a given temperature. In fact we can not know the actual size of an object, but can only know the size within a bracket (within the accuracy of our measuring equipment and technologies). So, while such puzzles are great for demonstration of physics and math, they don't and can not be considered to represent the real world. A more realistic suggested question would be, for example, ... At what angle of rotation within a degree will a wheel with a weight at top dead center rotate to before beginning the first oscillation back, excludding all forces except gravity and inertia. .. or ...How long within a second until the wheel settled to within 1° of bottom dead center. .... I am not saying anyone wasn't, but am reminding all to engineer with consideration that our calculations are done accordingly to charts and formulas based on data obtained from actual tests that have been considered and can not actually ever be truthfully duplicated in the real world. We must always allow for the fact that we are only accurate within some deviation. (something happened in my real life this past week which causes me to be big on this point at the moment). and... thank you for playing along. The worst suggestion of your lifetime may be the catalyst to the grandest idea of the century, never let suggestions go unsaid nor fail to listen to them. Modified by randykimball at Sun, Apr 01, 2007, 23:47:42

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Re: How would I go about....
Re: How would I go about.... -- cm	Post Reply	Top of thread	Forum

Posted by: randykimball ® 04/01/2007, 11:43:51 Author Profile eMail author Edit

?? If you put a weight on a wheel at the top and there are no forces to consider, the weight would cause the wheel to rotate until the wheel is at the bottom. 180°, half a circle: this is no puzzle. The worst suggestion of your lifetime may be the catalyst to the grandest idea of the century, never let suggestions go unsaid nor fail to listen to them.

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Re: Re: How would I go about....
Re: Re: How would I go about.... -- randykimball	Post Reply	Top of thread	Forum

Posted by: cm ® 04/01/2007, 12:06:11 Author Profile eMail author Edit

no puzzle???? I think your assumption is wrong. There would be a build up of momentum causing the wheel to rotate more than 180 degrees. I am not asking where it would come to rest, I am asking how far it would rotate before settling back to the bottom.

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Re: Re: Re: How would I go about....
Re: Re: Re: How would I go about.... -- cm	Post Reply	Top of thread	Forum

Posted by: rfox ® 04/01/2007, 14:28:32 Author Profile eMail author Edit

As far as I can tell this is still no puzzle. Assume bearing rotates about z-axis, y-axis is verticle, x-axis is horizontal. First condition: You put the weight directly on top of the wheel. Angle between the weight and the y-axis is zero. The force of the weight travels through the axis of rotation of the bearing and there is no rotation. Second condition: You put the weight on top of the wheel at a slightly offset angle (lets call it a) from the y-axis. If we neglect friction of the system, and Im assuming you are also neglacting drag of the system ( air friction), the wheel would rotate with the weight to exactly 360deg. - 2a before starting back towards its original position a. Your system would oscillate in the manner for t=infinity. Of course I could be totally wrong. LoL I took dynamics over a decade ago....

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Re: Re: Re: Re: How would I go about....
Re: Re: Re: Re: How would I go about.... -- rfox	Post Reply	Top of thread	Forum

Posted by: cm ® 04/01/2007, 15:04:33 Author Profile eMail author Edit

thanks rfox. why is it 2a? It's been over 20 years for me...lol

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Re: Re: Re: Re: Re: How would I go about....
Re: Re: Re: Re: Re: How would I go about.... -- cm	Post Reply	Top of thread	Forum

Posted by: rfox ® 04/01/2007, 15:23:58 Author Profile eMail author Edit

The wheel will rotate until its kenetic energy is 0 and its potential energy equals that of its original position at angle a. The point at which this happens is when the weight reaches the same angle a from y-axis, but on the opposite side. So the total angle the wheel has rotated about the z-axis (lets call it b) is: b = 360deg. - 2a

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