It would actually surprise me if any university had the ability to impose an overall bias in one of those directions over the other. There would seem to be too much variation among the individual professors, teachers, students, etc.

Anecdotally, I live in the shadow of a Big Ten university, so I know a lot of academics, and I don't think any of them have expressed a "follow the rules" approach that I was able to discern. Likewise for the people I know who are K-12 teachers, private music teachers, and so forth.

I don't know about any university, but at Caltech it was consistent that everything used was derived from first principles. There wasn't any "trust me, use this rule".

That wasn't consistent at my school, but classes that did derive everything from first principles were consistently the best ones.

I went to a small religious college, and my experience was similar to yours.

Edit: There were some exceptions, such as my double bass lessons.

I think it depends on the choice of professors and lots of good ones do teach in not so Ivy League but in regular city univs. I had 50/50 hit and misses with professors in my university. I think that's a decently good number too..

How would gear tooth profile affect MoI?

I just drew a box around half of the teeth. But the rest of the gear cross-section, being an airplane part, was sculpted to put material only where it was needed. Ideally, the strain at any point should be the same as any other point.

So the MoI was not simply a stackup of some stock shapes.

It's not that the calculation was particularly difficult, it's just that calculus was needed, and one couldn't just copy the formula for a stock shape.

It was just clear to me that some engineers were formula-pluggers and others learned it at a deeper level.

Stock shapes were certainly handy to check the math with, however. Fit the gear into a stock shape envelope, and have the gear envelope a stock shape. Your calculation should fall in between the results of those shapes.

The purpose of calculating the MoI was to determine if the stops at the end of the screw were strong enough to stop the gearbox without shattering.

>being an airplane part,

That explains it.

<g>

Airplane parts are a whole 'nother world. I imagine that rocket parts take that to the nth level, which is one reason that working on rockets is the ultimate for an engineer. A real engineer would pay to work on an F1 engine design <g>.

It would change the distribution of mass, presumably.