Question

Calculate the kinetic energy of energy of the Earth due to rotation about its own axis mass of the earth is 6 into 10 to the power 24 kg and radius of the earth is 6400 km moment of inertia of earth is 25 m squarecalculate the kinetic energy of the Earth due to rotation about its own axis mass of the earth is 6 into 10 to the power 24 kg and radius of the earth is 6400 km

Answer 1

kinetic energy = 1/2 mv^2
= 1/2 × 6×10^24×25 ×25
=1825×10^24 joule
may be that's ur answer

Answer 2

The rotational kinetic energy is $2.6\times10^{29}\ J$

Explanation:

Given that,

Mass of earth $M=6\times10^{24}\ kg$

Radius of earth $R=6400\ km$

Earth completes one rotation about its axis in 1 day.

We need to calculate the angular velocity

Using formula of angular velocity

$\omega=\dfrac{2\pi}{T}$

Put the value into the formula

$\omega=\dfrac{2\pi}{24\times60\times60}$

$\omega=7.27\times10^{-5}\ rad/s$

We need to calculate the rotational kinetic energy

Using formula of kinetic energy

$K.E=\dfrac{1}{2}I\omega^2$

$K.E=\dfrac{1}{2}\times\dfrac{2}{5}MR^2\times\omega^2$

Put the value into the formula

$K.E=\dfrac{1}{2}\times\dfrac{2}{5}\times6\times10^{24}\times(6.4\times10^{6})^2\times(7.27\times10^{-5})^2$

$K.E=2.6\times10^{29}\ J$

Hence, The rotational kinetic energy is $2.6\times10^{29}\ J$

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Topic : kinetic energy

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