Many Worlds Theory

Here’s a meme stolen borrowed from a young-Earth creationist:

First of all, why are so many creationists these days becoming flat-Earthers?

But secondly, does this meme even make sense to you?  I can understand (sort of) the confusion that a spinning tennis ball might bring: water is flung off the ball, rather easily, so why isn’t ocean water flung off the earth?  That’s a valid physics question.  But what in the name of Odin does this have to do with gravity?

Let’s do the physics.  Suppose there’s 0.25 kg of water on the ball to begin with (corresponding to roughly ½ cup).  The radius of a tennis ball is about 6.0 cm = 0.06 m.  The rotation rate of a served tennis ball is typically around 2200 rpm = 230 rad/s.  Therefore the linear velocity on the ball’s surface is v = ωr = 230 (0.06) = 13.8 m/s.  So the force needed to keep the water on the ball (i.e. to make it move in a circle contrary to Newton’s 1^st Law) is F = mv²/r = 0.25 (13.8)² / 0.06 = 794 N, which is about 178 pounds of force.  It’s not surprising the water is flung off: what force is there that could possibly do the trick?  The water would have to be “stuck” to the ball with a force of at least 794 N in order to stay in place.  (Gravity won’t do: the force of gravity between ½ cup of water and a tennis ball is easily found to be 2.7 x 10^–10 N, which is basically zero.)

OK, so what about water on the Earth?  The Earth is spinning, too.  Shouldn’t any water on the Earth’s surface be flung off?

Suppose I have half a cup of water on my desk.  Its mass is the same as in the previous example, but the radius of its motion is much bigger: 6,370,000 m, the radius of the Earth.  (I’m assuming for simplicity’s sake that I’m at the equator.)  Now, the half cup of water’s rotation rate is 1 revolution every 24 hours, or a rotational velocity of ω = 7.27 x 10^–5 rad/s.  Even though this is pretty small, we still get a fairly large v = ωr = 463 m/s.  That’s your (linear) velocity at the equator, and it’s pretty big.  So far, it still seems plausible that water might be flung off.

But wait:  how much force is needed to prevent this?  Well, F = mv²/r = 0.25 (463)² / 6,370,000 = 0.008 N, corresponding to the weight of less than a gram of mass.  Therefore, to not be flung off the Earth, a half cup of water needs only 0.008 N of force to be held in place.  Even without gravity, a tiny dab of scotch tape would be sufficient.  But there is gravity.  And in fact, gravity supplies a force of F = mg = .25 (9.8) = 2.45 N, or more than half a pound.

Seeing water flung off a tennis ball, it’s natural to wonder why water doesn’t get flung off a spinning Earth.  After all, we’re all moving pretty darn fast on this ride.  But the Earth’s radius is huge, so the force of gravity is more than adequate to keep things in place.  The fact that water is not flung off doesn’t mean gravity is a hoax, it means gravity is doing its fucking job.  The cure for this flat Earth bullshit is to take a basic physics class.

You fucking morons.

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