Can someone show me how to work this physics problem?

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 9.3 x 1019 J.Can someone show me how to work this physics problem?
Ok, kinetic energy can be related by the following formula:


1/2 x m x v^2 Where m is mass and v is velocity. For part (a) of your question we have to change this into the rotational notation so we get KE = 1/2 x I x (omega)^2 where I is the moment of inertia of the earth, and omega is the angular velocity in radians per second.





All you do from here is find the moment of inertia and the angular velocity of the earth and plug them into the second formula for part (a) and plug in the mass and linear velocity of the earth into the first formula for the answer to part (b).





If you need further breakdown or background post it and I'll respond again.





Cheers





Hahaha, also I just read Keith T's response above me and his rotational KE is way off, use the 1/2 x I x (omega)^2Can someone show me how to work this physics problem?
(b) can be calculated using simple kinetic energy and (1/2)mv^2.





However, you can't use this approach for (a) because the mass of the earth isn't all at the same distance from the earth's axis. Instead you need to use the moment of inertia for a solid sphere i = (2/5)mr^2 then the energy is


KE = (1/2)i(2*pi/T)^2


= (1/2)*(2/5)mr^2(2*pi/T)^2


= 0.8*m*(pi*r/T)^2


where m is the mass of the earth, pi is 3.14..., r is the radius of the earth, T is the period of rotation (24 hours).
Kinetic Energy is moving energy and it is given by the following formula (assuming of course non-relativistic energy which we have here).





KE = 1/2 m * v^2, where m is mass of moving object and v is the velocity.





so KE of earth rotation is


KE = 1/2 * mass of Earth * (velocity of rotation)


We can think of the velocity as distance/time, where distance traveled would be the Earth's circumference and time is one day since the Earth rotate about its axis in one day.





KE of Earth orbit about the sun would be similarly calculated but this time we use the Earth orbital circumference about the sun. Here the distance traveled around the sun is in one year.





KT

Yagi Antenna System For World Space