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)
mass of Earth, Me = 5.98*10^24 kg

radius, Re = 6.37*10^6 m

angular speed, w = 2*pi/T

Put values..

= 2*pi/(24*60*60)

= 7.3*10^-5 rad/s

moment of inertia of sphere, I = (2/5)Me*Re^2

put values..

= (2/5)*5.98*10^24*(6.37*10^6)^2

= 9.71*10^37 kg.m^2

rotational kinetic energy = (1/2)*I*w^2

put values..

= (1/2)*9.71*10^37*(7.3*10^-5)^2

= 2.6*10^29 J (Answer)

b) radius of orbit of earth around the sun, r = 1.496*10^11 m

time periode, T = 365 days

= 365*24*60*60

= 31536000 s

speed of earth around the sun, v = 2*pi*r/T

put values..

= 2*pi*1.496*10^11/31536000

= 29806 m/s

kinetic energy = 0.5*Me*v^2

put values..

= 0.5*5.98*10^24*29806^2

= 2.67*10^33 J (Answer)

I hope help you..