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Sagot :
The Earth's rotational kinetic energy is the kinetic Energy that the Earth
has due to rotation.
The rotational kinetic energy of the Earth is approximately 3.331 × 10³⁶ J
Reasons:
The parameters required for the question are;
Mass of the Earth, M = 5.97 × 10²⁴ kg
Radius of the Earth, R = 6.38 × 10⁶ m
The rotational period of the Earth, T = 24.0 hrs.
[tex]The \ moment \ of \ inertia \ of \ uniform \ sphere \ is \ I = \mathbf{\dfrac{2}{5} \cdot M \cdot R^2}[/tex]
Which gives;
[tex]\mathbf{I_{Earth}} = \dfrac{2}{5} \times 5.97 \times 10 ^{24} \cdot \left(6.38 \times 10^6 \right)^2 = 9.7202107 \times 10^{37}[/tex]
[tex]\mathrm{The \ rotational \ kinetic \ energy \ is} \ E_{rotational} = \mathbf{\dfrac{1}{2} \cdot I \cdot \omega^2}[/tex]
[tex]\mathrm{The \ angular \ speed, \ \omega} = \mathbf{\dfrac{2 \dcdot \pi}{T}}[/tex]
Therefore;
[tex]\omega = \dfrac{2 \cdot \pi}{24} = \dfrac{\pi}{24}[/tex]
Which gives;
[tex]\mathbf{E_{rotational}} = \dfrac{1}{2} \times 9.7202107 \times 10^{37} \times \left( \dfrac{\pi}{12} \right)^2 = 3.331 \times 10^{36}[/tex]
The rotational kinetic energy of the Earth, [tex]E_{rotational}[/tex] = 3.331 × 10³⁶ Joules
Learn more here:
https://brainly.com/question/13623190
The moment of inertia from part A of the question (obtained online) is that of the Earth approximated to a perfect sphere.
Mass of the Earth, M = 5.97 × 10²⁴ kg
Radius of the Earth, R = 6.38 × 10⁶ m
The rotational period of the Earth, T = 24.0 hrs
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