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Earth has a mass of 5.98 1024 kg and a radius of 6.38 106 m. Assume it is a uniform solid sphere. The distance of Earth from the Sun is 1.50 1011 m. (Assume Earth completes a single rotation in 24.0 hours and orbits the Sun once every 365 Earth days.) (a) What is the rotational kinetic energy of Earth on its axis

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Answer:

Explanation

Rotational kinetic energy of the earth = 1/2 Iω²

where I is moment of inertia of the earth and ω is angular velocity .

I = 2/5 m R² , m is mass and R is radius of the earth .

I = 2/5 x 5.98 x 10²⁴ x ( 6.38 x 10⁶ )²

=97.36 x 10³⁶

ω = 1 / T

T = 24 x 60 x 60 = 86400 s

ω = 1 / 86400

= 11.57 x 10⁻⁶ rad / s

Rotational Kinetic energy = 1/2 Iω²

= .5 x 97.36 x 10³⁶ x (11.57 x 10⁻⁶ )²

= 6516.54 x 10²⁴ J

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