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Object A is located on the floor at the equator.
Is that the magnitude of the normal force on A equal to its weight?

How to obtain an expression for normal reaction in terms of $m,g,r$ and $\omega$?

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The normal force from the floor (or the reading on a scale) would be N where: mg - N = mR$ω^2$. The, R, and, ω, are the radius and angular velocity of the earth.

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