Question

Calculate the KE that the earth has because of a) it's rotation about its own axis and b) its morion 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 US in one year is about 1.1 x 10^20 J.

Answer 1

Kinetic Energy about its own axis

Angular speed = 2π/T

Earth time period about its own axis T = 24 hours

So angular speed = 2π/(24×60×60) = 6.28/86400

Radius of earth R = 6400 km = 6400×103 m

Mass of earth M = 6×1024 kg

So moment of inertia of Earth = 2/5mR2

I = 2/5×6×1024×(6400×103)2 = 9830.4×1034 kgm2

Kinetic Energy = 1/2×9830.4×1034×(6.28/86400)2 = 25.97×1030 J

b.

K. E. = 1/2Iω2​​​​​​

I = mr2​​​​​​

r = distance of sun from earth = 15×1010 m

I = 6×1024×(15×1010)2 = 13.5×1046 kgm2​​​​​​

Angular speed = 2π/T

T = 365 days = 365×24×60×60 = 31536000 sec

Kinetic Energy = 1/2×13.5×1046×(2π/31536000)2 = 26.76×1032J