How many times Have you said, “I wish the days were longer”? Well, NASA scientists say that the construction of the Three Gorges Dam in China actually lengthened the days by slowing down the Earth’s rotation. Alleluia! Extra time you can operate to learn a fresh language, catch up on work, or even better, get some sleep.
This raises many questions. First of all, is it true? Did the dam actually make our day longer? And if so, why? And how much extra time are we talking about here? I mean, you have to plan your schedule, right? Should we build more giant dams to buy even more time?
Angular velocity
To answer these questions, we need three basic concepts in physics: (1) angular velocity, (2) angular momentum, and (3) moment of inertia. I will explain each of them.
First, a compact experiment that you can do yourself. If you have a swivel chair at your desk, swivel it with your feet off the ground and your arms tucked in. Now, before you throw up, stretch out your arms. It slows you down, right? Here’s the version with a man on a rotating platform:
Video: Rhett Allain
We call this rotational speed angular velocityrepresented by the Greek letter omega (Oh). Why “angular”? Below is a two-dimensional example. Think of this circle as the center xy coordinate plane. I drew a radius (R) to the point on the circle where it intersects the horizontal axis: