I am a little confused as to how the hell we are able to stay on a circular object that is spinning. I know it’s called Gravity but I am completeley in the dark as to how it works. Is it to do with our atmosphere, and if so how?
HELP!!
We are attracted to the Earth by the force of gravity. The force exists between any objects that have mass, and is proportional to the masses of the two objects and inversely proportional to the square of the distance between them. You don’t have to know the exact formula to realize that the Earth has a lot of mass, and we aren’t very far from it, so the gravitation force is significant.
Since the Earth is rotating, relative to a coordinate system that is moving with the Earth (that is, as things look to us) there is a centrifugal force that tends to throw us off the Earth. The magnitude of this force is proportional to our bodies’ mass, the rotational velocity, and the square of the distance from the center of rotation.
The distance from the center of rotation depends on where you are; the maximum is when you are standing in the equator, the minimum is when you are at either pole.
in any case, the maximum centrifugal force (at the equator) is 1/300 of the gravitational force. So we don’t fall off because there’s much more force pulling us towards the Earth than there is trying to throw us off.
The atmosphere has nothing to do with it.
Thanks for that, it’s been bugging me for a while.
So all a 300 pound man who lives at the North pole has to do to start his diet is move to the equator, where he would only weigh in at 299 pounds? Nobody tell Santa!
JonF said:
No. Centrifugal force is a fictitious force. It is an illusion caused by perspective. You “feel” a “centrifugal” force because of the effects of inertia.
Inertia is the principle that an object does not want to change behavior. You’ve heard about Newtons’s laws, and how an object in motion wants to remain in motion, an object at rest wants to remain at rest? That’s inertia.
The true situation is that your body is at a point on the surface of the earth. It wants to travel in a straight line at the same velocity as the surface of the earth. Only problem, the earth moves away from in in a circular path - the motion of its rotation. So what happens? Gravity is strong enough to pull you down and along with the surface of the Earth instead of floating away in a tangent (straight line). The force that affects your body is a centripetal force, or “center-seeking”. This force is gravity.
Actually, you don’t feel the “centrifugal” force because the gravitational force is much stronger, and the radius of curvature is so large. So speaking of centrifugal force is completely wrong.
The gist of the rest of the post is essentially true. You weigh slightly less at the equator than the poles because you have inertia fighting gravity. You weigh slightly less on top of a mountain than at sea level because you are further away from the center of gravity. However, the gravity field is not constant around the planet, there are local dips and surges. There’s a big discussion about this in Mailbag items in a thread discussing “What is ‘down’?”
As for what causes gravity, well that’s a very deep subject. A cursory explanation is to say it is a property of matter to have mass, and mass has gravity. A deeper answer takes an understanding of relativity, cosmology, and deep mathematics. Just say, “Uh, right,” unless you’re willing to commit to a degree in physics.
Well, opinions vary on whether or not centrifugal force is a real force. I’ll admit that most authorities call it a fictitous force. However, if you calculate in a rotating frame assuming there is a centrifugal force, then you’ll get the corect answer if you do the math right. I take the pragmatic view that centrifugal force can be called a real force.
That is certainly a way of looking at the situation. In the rotating reference frame of the Earth, the math is significantly trickier.
And, it’s easily proven that the correct answer is that your indicated weight (not your mass, obviously) is decreased by the Earth’s rotation. Calculating the magnitude of that effect is by far easiest by including centrifugal force. Examples of such calculations are at The MAD Scientist Network: Physics: How much would a 100 pound person weigh if the earth didn’t rotate?, Do you weigh differently at the North Pole than what you do at the equator?, and How much would we have weighed on Earth when its day was only 18 hours long?. And there is what Cecil has to say …
So, you don’t have to use centrifugal force if you don’t want to. Care to provide an example of calculating the efect of the Earth’s rotation on your weight without using centrifugal force? {grin}
Besides gravity’s counteracting our own inertia/centrifugal force there is also the fact that it does the same favor for the atmosphere around us, which keeps us from blowing back on our heels as might a little paper-clip man adhered to the surface of a magnetic ball in simulation of gravity but without the benefit of an atmosphere associated with his movement.
This is also the reason that when you drop an apple off the mast of a sailing ship it lands pretty much directly below you, as dropping it from a moving position effectively propels it forward with the same inertia as the ship has as it plows through the atmosphere.