Rotational Kinetic Energy Question (Regarding the Earth)

In summary, the conversation discusses finding the kinetic energy of the Earth orbiting around the Sun in joules, using the equation E rotation = (1/2)* I * w^2 where I is the moment of inertia and w is the angular velocity. The individual shares their solution, which calculates a rotational kinetic energy of 2.58×10^29 J, and asks if it is correct. The other person then clarifies that the question is actually asking for the translational kinetic energy of the Earth, which would be significantly greater than the rotational kinetic energy.
  • #1
zmoose27
1
0

Homework Statement



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

Homework Equations



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

where I = moment of Inertia
where w = angular velocity

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.
 
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  • #2
You found the rotational KE of the Earth revolving on its axis. But you were asked to find:
zmoose27 said:
What is the Kinetic Energy of the Earth Orbiting Around the Sun in Joules?
 
  • #3
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.
 

1. What is rotational kinetic energy?

Rotational kinetic energy is the energy an object possesses due to its rotation around an axis. In the case of the Earth, it refers to the energy caused by its spinning motion around its own axis.

2. How is rotational kinetic energy calculated?

The formula for calculating rotational kinetic energy is KE = (1/2)Iω², where I is the moment of inertia and ω is the angular velocity. In the case of the Earth, the moment of inertia is approximately 8 x 10^37 kgm² and the angular velocity is 7.27 x 10^-5 radians per second.

3. What factors affect the rotational kinetic energy of the Earth?

The rotational kinetic energy of the Earth is affected by its mass, moment of inertia, and angular velocity. Changes in any of these factors can alter the amount of rotational kinetic energy the Earth possesses.

4. How does rotational kinetic energy impact the Earth?

The rotational kinetic energy of the Earth plays a crucial role in maintaining its rotation and stabilizing its axial tilt. This affects the Earth's day and night cycle, seasons, and overall climate.

5. Can rotational kinetic energy be transferred to other forms of energy?

Yes, rotational kinetic energy can be converted into other forms of energy, such as heat or potential energy. This transfer of energy can occur through processes such as friction, tides, or the Earth's magnetic field.

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