Could a hydroelectric dam really make days longer?

How many times Did you say I wish the days were longer? Well, NASA scientists say the construction of the Three Gorges Dam in China has actually made the days longer, by slowing down the Earth’s rotation. Praise God! You can use the extra time to learn a new language, catch up on work, or even sleep better.

This raises a lot of questions. First of all, is this true? Has the dam really made our days longer? If so, why? And 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 have more time?

Angular velocity

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

First, here’s a little experiment you can do yourself. If you have a swivel office chair, have it swivel with your feet off the floor and your arms tucked in. Now, before you throw up, extend your arms. It slows you down, doesn’t it? Here’s a version with a human on a rotating platform:

Video: Rhett Allen

Rotational speed is what we call it Angular velocityIt is represented by the Greek letter Omega (Oh). Why “corner”? Here is a 2D example below. Think of this circle centered around xy Coordinate plane. I drew a radius (R) to a point on the circle where the horizontal axis intersects: