Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

Extracting energy from the Earth's rotation

As you know, the Earth spins around its central axis once every day, with a period of P = 86,400 s. We'll learn soon how to compute the moment of inertia of the Earth, but for now, we can take its value to be I = 9.7 x 1037 kg*m2.

  1. What is the angular velocity of the Earth?
  2. What is the rotational kinetic energy of the Earth?

My answers.

That sounds like a lot of energy

Now, the United States of America consumes a lot of energy each year, for transportation, heating, powering electric devices, and so forth. According to the US Energy Information Adminstration, in the year 2019, the US consumed a total of roughly EUS = 1 x 1020 J.

At the moment, we generate this energy by several methods, many of which are not very clean. Suppose -- just suppose -- that we could somehow extract some of the Earth's rotational energy and use it instead. That would cause the Earth's angular velocity to decrease, but perhaps the change might be too small for most people to notice or care. Let's find out.

We could compute the new angular velocity of the Earth in the following way.

  1. Write an equation for the new angular velocity of the Earth in terms of the other quantities.
  2. Compute the new angular velocity ωnew. (you will need to keep lots of digits in the calculations!)
  3. How long would the new period of the Earth's rotation be?
  4. Suppose we could generate energy in this way. Roughly how long could we continue to power the US before the length of the day increased by one second?

My answers.

Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.