# Re: GPT4 + Mathematica

```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
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