Centripetal Force vs Gravity

Sakha

I was learning a bit of centrifugal/centripetal forces, and then I asked myself. If at the equator, the Earth rotates at about 1,700 kilometers per hour, then why don't we go flying outside the earth due to the absence of centripetal forces. And if the gravity is enough to keep us on Earth, then the real acceleration due to gravity should be smaller because the centrifugal forces are pushing us outside the Earth.

Thanks in advance

matematikawan

The centripetal force per unit mass acting on the body at the equator is v²/R. This value is negligible compare to g=9.8 m/s².

atyy

Gravity is the centripetal force that keeps us from flying away. If gravity were to suddenly disappear, we would all immediately fly off tangentially to the earth's surface because of our angular momentum.

Yes, the real acceleration due to gravity is actually bigger than what we measure in a naive experiment. In a naive experiment, we don't take the rotation of the earth into account, and what we measure as g (say by using a pendulum) contains gravity and the centrifugal force due to the fact that we are in a rotating frame of reference.

matematikawan

I remember reading somewhere. It said that if the earth where to spin with twice the current rate(i.e. 12hrs) , we will be thrown into the outer space.

Today, is the earth spinning getting slower or faster ?

D H

There is no way to directly measure the acceleration due to gravity. This is a direct consequence of the weak equivalence principle, which has been verified to within a few parts per 10¹³, making this one of the most accurately verified of all physical laws. Gravity measurements are inherently indirect measurements because gravity is a fictitious force, just as is centrifugal force. Your "naive" experiments are the only kind of experiments that can be performed.

Off by nearly an order of magnitude. The Earth would have to rotate once per 1.41 hours, or 17 times faster than its current rate, and then only objects directly at the equator would be thrown into outer space.

Not too likely, since the Earth's rotation rate is slowing down. Asteroids are a different issue. Solar heating can make asteroids spin faster and faster through the YORP effect. Some asteroids spin so fast that they break apart, 1999 KW₄, for example.

matematikawan

Hi D H,

Of course you shouldn't believe me!. I didn't state the reference and I didn't went through the calculation. I'm nobody in the physicsforums. How do you guys obtained those awards ?