Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: chris on 11/07/2011 21:14:25
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At the poles the angular velocity is zero, while at the equator you are spinning around at about 1000 miles per hour. Therefore, does this have the effect of making you weigh less (owing to centrifugal effects) at the equator than at one of the poles?
Chris
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Yes the effect is about 0.3% or 3 grams per kilogram between the poles and the equator. Compare this with the reduction due to the bouyancy of the earth's atmosphere of 0.12% or 1.2 grams per kilogram for something approximately equal to the density of water
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Can you explain how you calculated that please?
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the effect is about 0.3%
nearer 0.5% if you include oblateness ...
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.
http://curious.astro.cornell.edu/question.php?number=310