Suppose two objects travel around the equator on Earth at the same speed, $v$, in opposite directions, where the speed $v$ is measured relative to the Earth's surface. Will they experience different centrifugal force due to already rotating Earth, and if so how big will the difference be?
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$\begingroup$ Hi Ruturaj. Your question has attracted several "close as unclear" votes, so I've edited it to try and make it clearer. If I have got the edit wrong, e.g. if you didn't mean the speed is relative to the Earth's surface, then please shout! $\endgroup$– John RennieCommented Jul 6, 2015 at 7:15
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If I understand your question correctly, they do experience a different centrifugal force. They both travel along the equator, with equal but opposite speed with respect to the surface of the earth. But the Earth frame itself is a rotating reference frame. So you could look at the problem in non-rotating frame, where one of the objects has a speed $u_1=v+v_\text{Earth}$ and the other one $u_2=v-v_\text{Earth}$. The force needed for the objects to stay on their circular path is $$ F=\frac{mu_{1,2}^2}{r}. $$ If they have the same mass, only their speeds differ, and they will experience different centrifugal forces.
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$\begingroup$ Thank you Daniel, my thoughts were that, there won't be any difference between centrifugal force experienced by objects, but I understood there will be a difference and given the radius of earth it will be very very small but certainly non-zero. $\endgroup$– RuturajCommented Jul 7, 2015 at 17:49