Let's say we put a human in a closed chamber which is going around a certain point at distance d from its center of mass at some angular velocity w.
The centrifugal force on a human will be w squared over r times his mass.
Is there any difference if the cause of this rotation is precession of a gyroscope connected to the chamber?
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$\begingroup$ It is unclear what you are asking. You seem to be mixing the effects of orbital motion with that of rotation. The short answer is that if the center of mass is not moving in a straight line, there must be a force that causes that. Can you elaborate a little more on the setup (maybe include a sketch) and describe the DOF that drive the kinematics of the system. $\endgroup$– John AlexiouCommented Mar 8, 2019 at 17:45
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$\begingroup$ Doesnt matter what force. Of course there is a force. Do you not know what precession is? $\endgroup$– Puppet masterCommented Mar 8, 2019 at 18:01
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$\begingroup$ In my mind precession is the slow rotation of the instantaneous rotation axis when it is not parallel to one of the principal rotation axes. $\endgroup$– John AlexiouCommented Mar 8, 2019 at 18:51
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$\begingroup$ Yes. Slow relative to the rotation right? So doest really rave to be slow. I added a picture. $\endgroup$– Puppet masterCommented Mar 8, 2019 at 19:13
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$\begingroup$ So if you fix a reference frame at the end of the gyroscope, and the frame is not itself rotating, only precessing, how many Gs of force will the person inside feel? $\endgroup$– Puppet masterCommented Mar 8, 2019 at 19:14
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1 Answer
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A reference frame rotating at the rate of a precessing gyroscope is still a rotating reference frame. It is not inertial. All of the usual effects in a rotating reference frame will be present including the usual centrifugal force.
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$\begingroup$ I do not think so. There should be according to newstons laws. But I don't think there is $\endgroup$ Commented Mar 9, 2019 at 16:41
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$\begingroup$ So which of Newton’s laws do you think is wrong in this case and exactly how do you think it fails? $\endgroup$– DaleCommented Mar 9, 2019 at 17:58
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$\begingroup$ No single one, Newtons laws don't work in all frames of reference all by them selves , to make the theory work you need to add some "inertial " forces. In this case there seems to be a contradiction with the Newtonian mechanics as you are in an accelerating frame and there at least in my opinion should be no inertial forces present. $\endgroup$ Commented Mar 9, 2019 at 19:26
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$\begingroup$ There are inertial forces in this frame, specifically the centrifugal and the Coriolis forces. $\endgroup$– DaleCommented Mar 9, 2019 at 20:12
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$\begingroup$ Have you ever seen a gyroscope precessing on a toy Eiffel tower as a pivot? $\endgroup$ Commented Mar 9, 2019 at 20:31