On Sun, Apr 9, 2023 at 3:11 PM smitra <smi...@zonnet.nl> wrote: >>* GPT: **For a solid sphere of uniform density, we can divide it into >> small* >> * volume elements, each with mass dm. The volume element located at a >> distance r from the center of the sphere has a moment of inertia relative >> to the x-axis given by:dIx = dm * y^2* > > *> smitra: dIz = dm * (x^2 + y^2)*
I asked GPT to take a second look at the part where it said "*dIx = dm * y^2*". I did NOT say it was wrong or it had made an error of any kind, I just asked it to look at it, but nevertheless it knew it had made a boo-boo. GPT said this: *"GPT: I apologize for the error in my previous response. The correct expression for the moment of inertia of a small volume element relative to the x-axis is:dIx = dm * (y^2 + z^2)This takes into account the fact that the mass element is not necessarily located on the y-axis, but rather at a distance y from the x-axis and at a distance z from the z-axis. Similarly, the moment of inertia of a small volume element relative to the y-axis is:dIy = dm * (x^2 + z^2) and the moment of inertia of a small volume element relative to the z-axis is:dIz = dm * (x^2 + y^2)I hope this clarifies the issue. Thank you for bringing it to my attention."* By the way, the version of GPT I was using was NOT the one that had the Mathematica plug-in. John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis> 5vd -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv3iiA7TsfSf-ujmv1Le1Syhh-cigi5OTcU4qxcNSN%2Btvw%40mail.gmail.com.
