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| Hi! Thanks for your help on my previous question concerning centrifugal force. I have another question about that: Assuming that one has a cone rotating at some speed on earth's surface, with gravity pointing directy down, would it be possible to have the same spheres that I talked about in my last question support a larger mass? LET ME EXPLAIN: So, you have your cone, and you have a few rotating spheres inside that cone, let's say 4 rotating spheres. Those sphere rotate inside of the cone where gravity and the upward accelerating of the cone cancel out. Now on those spheres is a platform that is allowed to rest on the rotating spheres. The rotating sphere rest inside carved out heim-spheres inside that platform, thus supporting the platform. NOW FOR MY FIRST QUESTION: would the spheres still rotate at the same distance away from the center of the cone? I think yes, because gravity and the upward acceleration of the cone still cancel out. AM I RIGHT? Now let's say a mass is allowed to rest on the rotating platform that is supported by the rotating spheres... Is the entire mass of the spheres, platform, and mass still "cancelled out" due to my thinking in the first question? Now for my last and most important question: What if a non- rotating platform and mass rest upon those rotating spheres, is the entire mass still supported? In ohter words, because the spheres rotate at a point in the cone where gravity is cancelled out due to the cones upward acceleration, the spheres do not have any more measurable weight. But would that still hold true for a non-rotating platform on the rotating spheres, and the mass on the platform? Please let me know. Any info will be accepted, sorry for this super-long question, but THANK YOU SO MUCH FOR YOUR HELP!!!
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| Question Date: 2009-07-02 | | Answer 1:
Based on the derivations we made last week, yes, the height of the balls in the cone is determined by the acceleration due to gravity and the spinning of the cone, not by the weights involved. What changes is the amount of force necessary to keep the cone spinning at the required speed; if you were to simply put the platform on the balls, the whole system would slow down due to the conservation of angular momentum (the platform has to spin, too). This brings up the fact that the platform is going to cause friction with the balls, and the more weight is on the platform, the stronger this friction will be. Once again, more force will be required to keep the cone spinning, and the platform will have to spin as well (and it will spin with the same angular velocity as the spheres). Unfortunately, there has to be friction in the system in order to keep it running: the reason why the balls revolve around the side of the rotating cone instead of just rolling to the bottom is because they experience friction with the sides of the cone. If the spheres are exerting a frictional force on the cone, then they will also exert friction on the platform, and will cause it to spin, too. You can't have the platform rest on the spheres without it starting to spin as well.
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