Question

If the earth has no rotational motion, the weight of a person on the equator is $W$. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight $\frac{3}{4}W$. Radius of the earth is $6400km$ and $g=10m/s^2$

Answer 1

g'= New gravitational acceleration

W= angular velocity

g' = g - $W^{2}R$ $co{s}^2\theta$

$\frac{3g}{4}=g-W^{2}R$

$W^{2}R=\frac{g}{4}$

W = $\sqrt{\frac{g}{4R}}$

= $\sqrt{\frac{10}{4\times 64w\times {10}^3}}$

= $\frac{1}{2\times 8\times 100}$

= $\frac{1}{1600}$

= $\frac{1}{16}\times {10}^{-2}$

= $0.6\times {10}^{-3}$