Question

Calculate the kinetic energy that the earth has because of (a) its rotation about its own axis and (b) its motion around the sun. Assume that the earth is a uniform sphere and that its path around the sun is circular. For comparison, the total energy used in the United States in one year is about 1.1 x 1020 J.

Answer 1

(a) KE(rot) =I ω²/2
I=2MR²/5
ω=2π/24•3600 = ...(rad/ s)
Earth’s mass is M = 5.97•10²⁴kg,
Earth’s radius is R = 6.378•10⁶ m.
(b)

Linear velocity of the Earth is
v=ωr = 2π• 1.496•10¹¹ /365•24•3600 = …m/s
KE=Mv²/2 =5.97•10²⁴• (2π• 1.496•10¹¹ /365•24•3600)²/2 = …J

Answer 2

Thanks!! Clears up everything