Question

Find the acceleration of a particle placed on the surface of the earth at the equator due to the earth's rotation. The diameter of the earth is $12800km$ and it takes $24$ hours for the earth to complete one revolution about its axis.

Answer 1

Diameter of earth $=12800km$

Radius $R=6400km=64\times {10}^{5}m$

The linear speed of the point on the surface of the earth:

$V=\frac{2\pi R}{T}$

$=\frac{2\times 3.14\times 64\times {10}^8}{24\times 3600}m/sec=465.185$

The acceleration can be given as:

$a=\frac{V^2}{R}=\frac{{\left(46.5185\right)}^2}{64\times {10}^5}=0.0338m/{sec}^2$