# Homework Help: Rotational Kinetic Energy Question (Regarding the Earth)

1. Jul 8, 2008

### zmoose27

1. The problem statement, all variables and given/known data

What is the Kinetic Energy of the Earth Orbiting Around the Sun in Joules?

2. Relevant equations

E rotation = (1/2)* I * w^2

where I = moment of Inertia
where w = angular velocity

3. The attempt at a solution

Well, this is my predicament: I don't know whether my professor wants me to use the above equation or not, but I don't know any other way to solve it. My answer is comes out to somewhere around 10^29, while his is around 10^33. So obviously something must be wrong....

My solution:
Earth's period = 23.93 hours
Therefore, its angular velocity is 7.29×10^ -5 rad·s-1.
Assuming that the Earth is perfectly spherical and uniform in mass density, it has a moment of inertia, I = 9.72×10^37 kg·m2.
Therefore, it has a rotational kinetic energy of 2.58×10^29 J.

Is this right? Or am I missing something completely?

Thanks a lot.

2. Jul 8, 2008

### Staff: Mentor

You found the rotational KE of the Earth revolving on its axis. But you were asked to find:

3. Jul 8, 2008

### calef

And if you think about it, it makes sense that the earth's translational kinetic energy is several orders of magnitude greater than its rotational. In fact, if you were only solving the net kinetic energy of the earth to a couple decimal places, you could neglect the rotational kinetic energy entirely.