Rotational Work & Energy problem

[colton4286]

The Question:

Calculate the kinetic energy (KE) 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 arond the sun is circular. For comparison, the total energy used in the U.S. in one year is about 9.3 X 10^19 J.

I know that the KE of a rigid object is 1/2*(moment of inertia)*(angular vel.)^2 but how to go solve for KE w/o given any of this info?

 

[Hootenanny]

The Question:

Calculate the kinetic energy (KE) 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 arond the sun is circular. For comparison, the total energy used in the U.S. in one year is about 9.3 X 10^19 J.

I know that the KE of a rigid object is 1/2*(moment of inertia)*(angular vel.)^2 but how to go solve for KE w/o given any of this info?

Hi colton and welcome to PF,

You are given sufficient information to answer this problem, perhaps the only thing that is missing is the mass of the earth, but we can look that up. Let's start with (a), just the rotation about it's own axis. The question states that we can assume that the Earth is a uniform sphere, so what is the moment of inertia of a sphere about it's own axis?

We also know (or can work out very easily) the angular velocity of the Earth since we know it's period of rotation.

For future reference we have the https://www.physicsforums.com/forumdisplay.php?f=152" specifically for such questions. A moderator will move this thread there shortly so there's no need to start a new thread in there now.

 

[physixguru]

the following questions to yourself shall help a great deal::

What is the time period expression for a rotating body?
Now, what is the time period of Earth's rotation about its own axis ?( come on it is a general knowledge question).
Mass of earth= 6 *10^24 kg
Radius= 6400*10^3 m
What is the moment of inertia of a spherical body?

Kickstart buddy!