@JeremyDover, now I see where the inspiration came from :)

Also, are you going to write a "Making of"? The extraction and the re-use of letters is really cool and seems hard to make

@bobble Yep! I needed to keep it on the down low.

I guess I could...there weren't any special techniques, just a lot of trial and error. Mostly error.

Well, that's basically what I put in my "Making of" :P

@bobble I think there are two things going on here. The first is the contribution of the weight of the object; the centripetal force that keeps it going round in a circle is the sum of the tension in the string and the weight of the object, which means that at fixed speed the tension will need to be bigger at the top than at the bottom.

The second is that conservation of energy says that the object will have to be moving slower at the top than at the bottom.

(Which means less centripetal force at top than bottom, which again means that the string tension will be less at top than at bottom.)

Ah that makes sense

the teacher's keys just said that was how it worked and didn't explain why

I need to go to bed, so I'll leave you to work out the details. I hope you've been taught all the formulae you need.

shrugs it wasn't required to solve the problems

and yes, I got my formulas

Oh, OK.

Incidentally, "7N + 2N does not equal 15N", while of course true, wasn't quite the observation you wanted, which was "7N + 2N does not equal 15N - 2N".

(In case I wasn't explicit enough: slower at top than bottom because more gravitational potential energy there, hence less kinetic energy.)

thank you