Answer to Question #179469 in Classical Mechanics for Kat

Question

Assume that the earth’s rate of rotation were increased to such an extent that the

apparent weight of an object on the equator was zero. What would then be the period

of rotation of the earth?

Radius of the earth = 6380 km

Answer 1

Answer

$g^{'}=g-R\omega^2$

Given they $g^{'}=0kg/m^2$

So

$\omega=\sqrt{\frac{g}{R}}$

$\omega=\sqrt{\frac{9.8}{6380000}}$

And time period

$T=\frac{2\pi}{\omega}=\frac{2\pi}{\sqrt{\frac{9.8}{6380000}}}=4.1\times10^6s$