this post was submitted on 19 Nov 2024
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Acceleration vs. Velocity
Not quite. When you're rotating, you are constantly accelerating in a tangent direction to the diameter. So the poster is right that we should be feeling a force shooting us away from the center of earth.
Except the force of gravity cancels out the centripetal force and then some.
So [force of gravity] - [centripetal force of Earth's rotation] = 9.8m/s^2
The difference is about 0.5%. A mass weighing 100kg at the north pole would only weigh 99.5kg at the equator. Most of the difference is the centerfugal force of the earth's rotation.
I've not checked the numbers, but apparently it's detectable in Olympic sports. More height records get broken at equatorial latitudes that higher ones.
Interesting, would the muscles of someone living far away from the equator be stronger in general than compared to someone with the same genes / lifestyle on the equator?
0.5% is so tiny that it disappears into the noise. It's a 1 in 200 difference. In theory, it would make a difference. In practice, you won't be able to measure it. Other confounding factors would bury it.
That assumes a perfectly spherical earth. The earth is not perfectly spherical.
This. Planets are in hydrostatic equilibrium, meaning that the combined acceleration by gravity and the centrifugal "force" is equal all over the world (except for local differences due to mountains and dense crust).
Hydrostatic equilibrium yes, but equal? No. We agree that centrifugal force is a factor. Now ask yourself, why would gravity suddenly strengthen at the equator to get the surface acceleration to stay equal to that of the poles?
It doesn't. As a result the Earth seeks a new hydrostatic equilibrium, bulging out at the equator. This in turn strengthens the centrifugal force a bit while also slightly diminishing the force of gravity (because more of the planet's mass is farther away). So the same effect is taken even further. Local differences add a layer of noise on top of this, but the end result is that the net surface acceleration is measured to average slightly less at equatorial regions than at the poles, with for example Singapore getting 9.7639 m/s2 of downward acceleration, while Helsinki gets 9.825 m/s2.
You're right, I had it backwards. Hydrostatic equilibrium makes it that the combined force vector of gravity and the centrifugal force is perpendicular to the planet surface everywhere.
The fact that your units are units of acceleration proves the guys point, no?
It sounded like the guy meant the 1700km/h is a velocity, not an acceleration, which is why we don't feel the force of acceleration.
I was pointing out that spinning is acceleration, just in this case we can't feel it due to other forces.
Only on the equator, the force is just tiny, it produces major weather systems through the coriolis effect but only on giant scales. This would be like saying people get dizzy if they stand near the pole.
What are those pre-math numbers though? How screwed would we be if rotation doubled or stopped (regardless of the virtual impossibility)?
Have you seen the elementary school experiment where you spin an egg on a flat surface, then you stop the egg and let it go and the then the egg starts spinning again?
If the earth suddenly stopped spinning, the atmosphere would still be spinning at 1700km/h.
A cat 5 hurricane has wind speeds of 253km/h. So we'd be boned.
Look up xkcd world stop spinning
The actual amount of centrifugal force is also tiny. Sure, it's a relatively fast linear speed compared to something like a merry-go-round, but a merry-go-round's angular velocity is much higher, and that's the one you use when calculating the force trying to fling you off.
Also, centripetal force is the inward force observed by an external non-rotating reference frame which deflects motion into a curve. You've conflated it with centrifugal force, which is the outward "fictitious" force experienced in a rotating reference frame.