Question

An early major objection to the idea that Earth is spinning on its axis was that Earth would turn so fast at the equator that people would be thrown off into space. What centripetal force is needed for a person of mass 80.9 kilograms at the equator? The radius of Earth is about 6390 kilometers. Include units in your answer. Answer must be in 3 significant digits.

Answer 1

We will have the following:

$F=\frac{mv^2}{r}$

Then we determine the rotation of Earth:

$\frac{2\pi}{24h}=\frac{2\pi}{1440\min}=\frac{2\pi}{86400s}\approx0.0000727Hz$

Then:

$v=r\omega\Rightarrow v\approx(6390\operatorname{km})(0.0000727)$$\Rightarrow v\approx0.464553\operatorname{km}/s\Rightarrow v\approx464.553m/s$

Now, we find the force:

$F\approx\frac{(80.9Kg)(464.553m/s)^2}{(6390000m)}\Rightarrow F\approx2.732235951\ldots N$$\Rightarrow F\approx2.73N$

So, the force needed would be approximately 2.73N.