1. Tardigrade
  2. Question
  3. Physics
  4. With what angular velocity the Earth should spin in order that a body lying at 45° latitude may become weightless?

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. With what angular velocity the Earth should spin in order that a body lying at $45^{\circ}$ latitude may become weightless?

Gravitation

Solution:

$g'=g-\omega^{2} \cdot R \cos ^{2} \lambda$
if $g'=0$ at $\lambda=45^{\circ}$
$ \Rightarrow \omega^{2} R \cos ^{2} 45^{\circ}=g$
$\omega^{2} R\left(\frac{1}{2}\right)=g$
$ \Rightarrow \omega=\sqrt{\frac{2g}{R}}$