May the Forces Be With You

Gravity and the Centrifugal Force

Notes

Here's how the total force decomposes into gravity and centrifugal force. When calculated along the surface of the Earth, the force of gravity and the centrifugal force are much, much larger than the residual force the remains after they nearly cancel out - without the centrifugal force, the Mississippi would flow very rapidly northward, emptying the Gulf of Mexico into the center of North American.

But more importantly, if the Earth's rotation were stopped, the potential energy of loose material on the surface of the Earth would be very great - and that potential energy would be converted to kinetic energy very rapidly as water, ice, soil, and rock started to flow toward the equator. That kinetic energy would in turn be converted to heat.

Just as a back of the envelope calculation - one kilogram of water at the pole would have potential energy of approximately 10 m/s/s*10,000 meters*1kg=100,000 J, which is enough energy to raise the temperature of a kg of water by about 25 degrees Celsius, so saying that the ground would melt is an exaggeration (when I first did this calculation I was off by a factor of 10). Still, I don't expect anyone to be living after the Earth starts relaxing to a new natural shape.

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