I had a doubt regarding centrifugal force on earth is not accounted in any equations as object falling towards earth.eg f=ma.i read questions asked by few about the same and got to a conclusion that value of g(9.8m/s^2) is a relative number derieved.but I still cant find it in gravitational force equation.why is that.or is my interpretation wrong.this might be a repetitive question. But please clarify.
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1Did you read the wikipedia article about gravity on earth? It explains the issue in detail. And please read your question at least once before submitting. – Alexander Nov 10 '13 at 13:22
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possible duplicate of Is acceleration due to gravity constant? – Danu Nov 10 '13 at 13:24
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Strictly speaking, Newtonian dynamics problems on the Earth's surface are done in an accelerated reference frame owing to the Earth's rotation. But often this acceleration is very small: at the equator (Earth radius $6.317\times10^6{\rm m}$) the centripetal acceleration of a body on the Earth's surface is
$$\omega^2 R = \left(\frac{2\,\pi\,{\rm rad}}{24\times 3600{\rm s}}\right)^2 \times 6.317\times10^6{\rm m} = 0.033{\rm m\,s^{-2}}$$
or about three thousands of the acceleration owing to gravity. So for many dynamics questions it makes little difference to the outcome, depending on the accuracy you need.
However, an important example where it is important is in meteorology: the accelerated frame begets also the Coriolis Force (see the Heading "Meteorology" in the Coriolis Effect Wikipedia Page) and this has a huge impact on weather systems.
In General Relativity, the momentarily comoving inertial frames at the surface of the Earth are heading through the Earth's surface, accelerating relative to the later at $g$ towards the Earth's centre if you're sitting on the Earth's surface. Acceleration in a certain sense is never relative: if you and another observer begin from the same point at $t=0$ in frames that are accelerating relative to one another and if you are both carrying the appropriate system of accelerometers, your accelerometers will always tell the two frames apart (i.e. give different readings) - a situation quite unlike when two observers both move in inertial frames (all local experiments would turn out the same for both observers).
Selene Routley
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