Respuesta :
Answer
Given,
Mass of the Uranus, M = 8.68 x 10²⁵ Kg
Radius of Uranus, R = 2.56 x 10⁷ m
Distance of Uranus, D = 2.87 x 10¹² days
a) Rotational Kinetic energy of the Uranus
moment of inertia of the Uranus
[tex]I = \dfrac{2}{5}MR^2[/tex]
[tex]I = \dfrac{2}{5}\times 8.68\times 10^{25}\times (2.56\times 10^7)^2[/tex]
I = 22.75 x 10³⁹ kg.m²
Angular speed
[tex]\omega = \dfrac{2\pi}{T} = \dfrac{2\pi}{17.3\times 3600}[/tex]\
[tex]\omega = 1 \times 10^{-4}[/tex]
Rotational Kinetic energy
[tex]KE = \dfrac{1}{2}I\omega^2[/tex]
[tex]KE = \dfrac{1}{2}\times 22.75\times 10^{39}\times (10^{-4})^2[/tex]
[tex]KE = 11.38\times 10^{31}\ J[/tex]
b) Rotational Kinetic energy of Uranus in its orbit around sun
moment of inertia of the Uranus
[tex]I = \dfrac{2}{5}MR^2+ Ma^2[/tex]
[tex]I = 22.75\times 10^{39}+ 8.68\times 10^{25}\times (2.87\times 10^{12})^2[/tex]
I = 7.15 x 10⁵⁰ kg.m²
Angular speed
[tex]\omega = \dfrac{2\pi}{T} = \dfrac{2\pi}{3.08\times 10^4\times 3600\times 24}[/tex]\
[tex]\omega =2.36\times 10^{-9}[/tex]
Rotational Kinetic energy
[tex]KE = \dfrac{1}{2}I\omega^2[/tex]
[tex]KE = \dfrac{1}{2}\times 7.15\times 10^{50}\times (2.36\times 10^{-9})^2[/tex]
[tex]KE = 1.99\times 10^{33}\ J[/tex]
