The rotational kinetic energy of the Earth due to rotation about its axis is [tex]2.56\times 10^{29} \;Joules .[/tex]
Given the following data:
Radius of Earth = 6371 km = [tex]6.371\times 10^6\;m.[/tex]
Mass of Earth = [tex]5.972\times 10^{24} kg[/tex]
Distance of Earth from Sun = 149,600,000 km.
How to calculate the kinetic energy of the Earth.
Mathematically, the rotational kinetic energy of the Earth due to rotation about its axis is given by this formula:
[tex]K.E_{rot}=\frac{1}{2} I\omega^2[/tex] .....equation 1.
Where:
- I is the moment of inertia.
- [tex]\omega[/tex] is the angular velocity.
Note: Earth is spherical in shape.
For a solid sphere:
Mathematically, the moment of inertia of a solid sphere is given by this formula:
[tex]I=\frac{2}{5} mr^2[/tex] .....equation 2.
Substituting eqn. 2 into eqn. 1, we have:
[tex]K.E_{rot}=\frac{1}{2} (\frac{2}{5} mr^2)\omega^2\\\\K.E_{rot}=\frac{mr^2 \omega ^2}{5} \\\\K.E_{rot}=\frac{5.972\times 10^{24} \times (6.371\times 10^{6})^2 (\frac{2\pi}{24 \times 60} )^2}{5}\\\\K.E_{rot}=2.56\times 10^{29} \;Joules[/tex]
Read more on moment of inertia here: https://brainly.com/question/3406242
