Can a Hydroelectric Dam Really Make the Days Longer?

How many times have you said, “I wish the days were longer”? Well, NASA scientists say the construction of China’s Three Gorges Dam actually did make the days longer, by slowing the rotation of the Earth. Hallelujah! Extra time you can use to learn a new language, catch up at work, or even better, sleep in.

This raises a lot of questions. First of all, is it true? Did the dam actually make our days longer? And if so, why? And just how much extra time are we talking about here? I mean, you need to plan your schedule, right? Should we build more giant dams to get even more time?

Angular Velocity

To answer these questions, we need three basic physics ideas: (1) angular velocity, (2) angular momentum, and (3) the moment of inertia. I’ll explain each of these.

First, here’s a little experiment that you can do yourself. If you have a rotating desk chair, get it spinning with your feet off the ground and your arms tucked in. Now, before you throw up, extend your arms. It slows you down, right? Here’s a version with a human on a rotating platform:

Video: Rhett Allain

The speed of rotation is what we call angular velocity, represented by the Greek letter omega (ω). Why “angular”? Here’s a two-dimensional example below. Think of this circle as centered on an xy coordinate plane. I’ve drawn a radius (R) to a point on the circle where it cuts the horizontal axis: