Centripetal Force and Gravity: Exploring the Equator Paradox

In summary, the Earth is spinning slower than it used to, and we would only be thrown out of the Earth if it suddenly speeded up.
  • #1
Sakha
297
0
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
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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 ?
 
  • #5
atyy said:
Yes, the real acceleration due to gravity is actually bigger than what we measure in a naive experiment.
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.

matematikawan said:
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.
Off by nearly an order of magnitude. The Earth would have to rotate http://www.google.com/search?q=2*pi/(sqrt(9.8m/s^2/6378km))&btnG=Search", 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 http://www.space.com/scienceastronomy/asteroid_spin_030910.html" [Broken], for example.
 
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  • #6
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 ?
 

1. What is the difference between centripetal force and gravity?

Centripetal force is the force that acts towards the center of a circular motion, keeping an object moving in a circular path. Gravity, on the other hand, is the force of attraction between two objects due to their masses. While both forces can cause circular motion, they act in different ways.

2. Which force is stronger, centripetal force or gravity?

In most cases, gravity is the stronger force. This is because the force of gravity is directly proportional to the mass of the objects, while centripetal force is dependent on the speed and radius of the circular motion.

3. How do centripetal force and gravity work together?

Centripetal force is responsible for keeping an object moving in a circular path, while gravity is responsible for pulling that object towards the center of the circular motion. In a stable orbit, these two forces work together to keep an object in a circular path around a larger object.

4. Can an object experience centripetal force without gravity?

Yes, an object can experience centripetal force without gravity. This can occur in cases where an object is moving in a circular path due to a different force, such as tension in a string or the force of a person's hand.

5. How is centripetal force related to circular motion?

Centripetal force is necessary for an object to maintain circular motion. Without a centripetal force acting towards the center of the circular path, the object would move in a straight line tangent to the circle.

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