Question

If earth stops spinning about its own axis, what will be the change in acceleration due to gravity on its equator? the radius of earth is $6.4\times {10}^{6}m$ and its angular speed is $7.27\times {10}^{-5}rad/s$.

Answer 1

Effective acceleration due to gravity is given by
$g^{\prime }=g-R{\omega }^2{\cos }^2\theta$.
Hence, change in acceleration due to gravity is given as
$△g=g^{\prime }-g=-R{\omega }^2{\cos }^2\theta$,
At equator $\theta =0$.
Hence, $g^{\prime }-g=-R{\omega }^2$
$=-6.4\times {10}^6\times (7.27\times {10}^{-5}{)}^2=-0.0338m/s^2$
$g^{\prime }-g=-3.38cm/s^2$
The negative sign signifies that, the decrease in gravitational acceleration is due to the rotation of earth.