Additionally, gravity grows weaker as you get higher, but in this model, "gravity" gets stronger as you go higher.
does it?
"Gravity grows weaker as you get higher."
The gravitational acceleration on Mount Nevado Huascarán, Peru at an altitude of 6,768 m is 9.7639 2
and the gravitational acceleration in Lima, Peru at an altitude of 154 m is 9.782631 m/s2.
That makes sense.
And on that "model, 'gravity" gets stronger as you go higher" because the acceleration due to the rotary motion is inversely proportional to the radius.
Yeah, because tangential acceleration = v2/r ~ 1/r.
And v is the linear speed, given by v = ωr (ω is the rotation speed).
Well, so also v2/r = (ωr)2/r = ω2r ~ r.
So which one do I use, the top one or the bottom one?
The top one because all parts of the earth (be it a Globe or a "What if?") rotate with the same angular velocity, ω.
But there's no ω at all in the top one, so how do you keep it constant? There's only v, which might or might not change with r when angular velocity is constant.
How do I wriggle my way out of this? Guess I don't and just say sorry, I wasn't thinking straight when I said:
"And on that "model, 'gravity' gets stronger as you go higher" because the acceleration due to the rotary motion is inversely proportional to the radius."
It should have been,
"And on that "model, 'gravity" gets stronger as you go higher" because the acceleration due to the rotary motion is proportional to the radius.".
On that "What if?" version higher altitude is closer to the centre of rotation, so has a slightly higher "gravity".
And, of course, my answer to your
So which one do I use, the top one or the bottom one?
Should have been, "The bottom one because all parts of the earth (be it a Globe or a "What if?") rotate with the same angular velocity, ω".
They do (or should) say that "One should put brain into gear before touching keyboard".