Question

what is the rotational kinetic energy of the earth? use the moment of inertia you calculated in part a rather than the actual moment of inertia given in part b.

Answer 1

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.

$The \ moment \ of \ inertia \ of \ uniform \ sphere \ is \ I = \mathbf{\dfrac{2}{5} \cdot M \cdot R^2}$

Which gives;

$\mathbf{I_{Earth}} = \dfrac{2}{5} \times 5.97 \times 10 ^{24} \cdot \left(6.38 \times 10^6 \right)^2 = 9.7202107 \times 10^{37}$

$\mathrm{The \ rotational \ kinetic \ energy \ is} \ E_{rotational} = \mathbf{\dfrac{1}{2} \cdot I \cdot \omega^2}$

$\mathrm{The \ angular \ speed, \ \omega} = \mathbf{\dfrac{2 \dcdot \pi}{T}}$

Therefore;

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

Which gives;

$\mathbf{E_{rotational}} = \dfrac{1}{2} \times 9.7202107 \times 10^{37} \times \left( \dfrac{\pi}{12} \right)^2 = 3.331 \times 10^{36}$

The rotational kinetic energy of the Earth, $E_{rotational}$ = 3.331 × 10³⁶ Joules

Learn more here:

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