Posted: 1/14/2012 7:41:54 AM EDT
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Why isn't relative gravity appreciably weaker at the equator versus at the poles?
When we stand on the earth, the centripetal force of gravity is counteracted by the centrifugal force of the rotating of the planet. If we're standing on the pole, we aren't rotating, therefore we aren't being counteracted by the centrifugal force. So we should be much heavier. This is obviously not the case. I seem to have slept through this portion of high school physics. What the hell simple thing am I missing? |
| The effective acceleration of gravity at the poles is 980.665 cm/sec/sec while at the equator it is 3.39 cm/sec/sec less due to the centrifugal force. If you weighed 100 pounds at the north pole on a spring scale, at the equator you would weigh 99.65 pounds, or 5.5 ounces less. |
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Nah you guys are missing what I'm asking.
If you ride the gravitron, the centrifugal force pushes you against the wall. If you were to sit on the roof of it in the very center, you would just spin in circles, but aren't pulled in any direction. Since earth's gravity is constantly pulling us inward, we should be getting pulled harder towards the ground when we aren't flying around the equatorial line at high speed(counteracting the gravity). |
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The effective acceleration of gravity at the poles is 980.665 cm/sec/sec while at the equator it is 3.39 cm/sec/sec less due to the centrifugal force. If you weighed 100 pounds at the north pole on a spring scale, at the equator you would weigh 99.65 pounds, or 5.5 ounces less. Is the centrifugal force really that weak? I would have expected it to be much stronger than that. |
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http://curious.astro.cornell.edu/question.php?number=310
You are right, that because of centripetal acceleration you will weigh a tiny amount less at the equator than at the poles. Try not to think of centripetal acceleration as a force though; what's really going on is that objects which are in motion like to go in a straight line and so it takes some force to make them go round in a circle. So some of the force of gravity is being used to make you go round in a circle at the equator (instead of flying off into space) while at the pole this is not needed. The centripetal acceleration at the equator is given by 4 times pi squared times the radius of the Earth divided by the period of rotation squared (4*pi2*r/T2). The period of rotation is 24 hours (or 86400 seconds) and the radius of the Earth is about 6400 km. This means that the centripetal acceletation at the equator is about 0.03 m/s2 (metres per seconds squared). Compare this to the acceleration due to gravity which is about 10 m/s2 and you can see how tiny an effect this is - you would weigh about 0.3% less at the equator than at the poles! There is an additional effect due to the oblateness of the Earth. The Earth is not exactly spherical but rather is a little bit like a "squashed" sphere, with the radius at the equator slightly larger than the radius at the poles (this shape can be explained by the effect of centripetal acceleration on the material that makes up the Earth, exactly as described above). This has the effect of slightly increasing your weight at the poles (since you are close to the centre of the Earth and the gravitational force depends on distance) and slightly decreasing it at the equator. Taking into account both of the above effects, the gravitational acceleration is 9.78 m/s2 at the equator and 9.83 m/s2 at the poles, so you weigh about 0.5% more at the poles than at the equator. |
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http://curious.astro.cornell.edu/question.php?number=310 You are right, that because of centripetal acceleration you will weigh a tiny amount less at the equator than at the poles. Try not to think of centripetal acceleration as a force though; what's really going on is that objects which are in motion like to go in a straight line and so it takes some force to make them go round in a circle. So some of the force of gravity is being used to make you go round in a circle at the equator (instead of flying off into space) while at the pole this is not needed. The centripetal acceleration at the equator is given by 4 times pi squared times the radius of the Earth divided by the period of rotation squared (4*pi2*r/T2). The period of rotation is 24 hours (or 86400 seconds) and the radius of the Earth is about 6400 km. This means that the centripetal acceletation at the equator is about 0.03 m/s2 (metres per seconds squared). Compare this to the acceleration due to gravity which is about 10 m/s2 and you can see how tiny an effect this is - you would weigh about 0.3% less at the equator than at the poles! There is an additional effect due to the oblateness of the Earth. The Earth is not exactly spherical but rather is a little bit like a "squashed" sphere, with the radius at the equator slightly larger than the radius at the poles (this shape can be explained by the effect of centripetal acceleration on the material that makes up the Earth, exactly as described above). This has the effect of slightly increasing your weight at the poles (since you are close to the centre of the Earth and the gravitational force depends on distance) and slightly decreasing it at the equator. Taking into account both of the above effects, the gravitational acceleration is 9.78 m/s2 at the equator and 9.83 m/s2 at the poles, so you weigh about 0.5% more at the poles than at the equator. Excellent. Thanks very much! |
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The effective acceleration of gravity at the poles is 980.665 cm/sec/sec while at the equator it is 3.39 cm/sec/sec less due to the centrifugal force. If you weighed 100 pounds at the north pole on a spring scale, at the equator you would weigh 99.65 pounds, or 5.5 ounces less. Is the centrifugal force really that weak? I would have expected it to be much stronger than that. You have to remember that your body is already traveling the same speed as the surface of the earth. And the surface is relatively flat. So your body is already 'flying' along a sorta flat surface in realation to distance so it's not like the earth is trying to fling you out into space as it spins, because if it suddenly stopped you'd fly along the earths surface for a few hundred miles before starting to drift off into space. Think of it like this, if you have a string with a ball on it and your spinning it above your heal like a helocopter and let go, it dosent go straight out 90 degrees from your hand, it flys whatever direction it was facing when you let go. It's like flying in a plane, your not traveling at 500mph, your traveling at 56,500mph if you fly east, and 55,500mph if you fly west  (in relation to a stationary point in space)
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It's is. You will weigh less at the equator. Other way around...weigh less at the poles & more at the equator, the Earth is not a perfect sphere, it is like most of us...wider across the mid line. Which is why some mountain in South America is actually "taller" than Mt. Everest as measured from the earth's center. |
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The effective acceleration of gravity at the poles is 980.665 cm/sec/sec while at the equator it is 3.39 cm/sec/sec less due to the centrifugal force. If you weighed 100 pounds at the north pole on a spring scale, at the equator you would weigh 99.65 pounds, or 5.5 ounces less. Is the centrifugal force really that weak? I would have expected it to be much stronger than that. The centripetal force is really that weak. 
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Quoted: Quoted: Quoted: The effective acceleration of gravity at the poles is 980.665 cm/sec/sec while at the equator it is 3.39 cm/sec/sec less due to the centrifugal force. If you weighed 100 pounds at the north pole on a spring scale, at the equator you would weigh 99.65 pounds, or 5.5 ounces less. Is the centrifugal force really that weak? I would have expected it to be much stronger than that. The centripetal force is really that weak. Tangential speed is high but that radial distance is also great. |
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Centrifugal force (from Latin centrum, meaning "center", and fugere, meaning "to flee") represents the effects of inertia that arise in connection with rotation and which are experienced as an outward force away from the center of rotation.
Centripetal force (from Latin centrum "center" and petere "to seek"[1]) is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. I believe I used that correctly. Centrifugal force would be what is keeping the water in the bucket as you spin it around on a string. Centripetal force would be what is making the bucket continue to orbit its anchor. Right? |