Do Hydroelectric Dams Have the Power to Extend Our Days?

Have you ever mused about having more hours in a day? According to NASA, the construction of China's colossal Three Gorges Dam has achieved just that by decreasing Earth's rotational speed. Imagine the possibilities with those few extra moments for learning, working, or simply reveling in more sleep!

This intriguing claim sparks curiosity. Did the dam truly stretch the length of our days? And by what mechanism did this occur? How significant is this additional time? Could the building of more massive dams further augment our days?

Understanding Angular Velocity

To grasp the answers, you need to understand three core physics concepts: angular velocity, angular momentum, and the moment of inertia. Let's delve into these topics.

Consider an experiment with a swiveling office chair. Spin yourself with your feet off the floor and arms retracted. When you extend your arms, does the spin slow down? That's angular velocity at work.

Angular velocity, denoted by the Greek letter omega (ω), describes how fast an angle changes as a point rotates around a circle. Imagine a point circling counterclockwise, creating a sweeping angle relative to a horizontal line as it spins. The faster it travels, the quicker the angle transforms — this defines angular velocity.

In vehicle engines, this concept is mirrored in revolutions per minute (RPM), which reflects the number of full rotations the crankshaft completes within a minute.

The Concept of Moment of Inertia

Inertia represents an object's resistance to changes in its motion. Heavier objects, like a bowling ball compared to a baseball, resist motion changes more. When rotated, this principle is called the moment of inertia.

A car wheel and a bicycle wheel spin differently due to their moments of inertia. Although both may weigh the same, the bike wheel spins faster for a given push due to a lower moment of inertia.

Where mass is concentrated influences rotational inertia. Given two identically sized and weighted wheels, one with mass spread outward and another as a solid disk, the solid will spin more quickly due to a reduced moment of inertia.

Exploring Angular Momentum

Angular momentum, the product of angular velocity and moment of inertia, remains unaltered in isolated systems. Thus, if external forces don't interfere, changing the moment of inertia inversely affects angular velocity.

Dams and Earth's Rotation

Returning to our question: how does a dam affect Earth's rotation? The planet, an isolated spinning entity, maintains steady angular momentum. Changing the mass distribution on Earth, like with a dam, alters its inertia and thereby its spin rate.

A dam prevents water from naturally flowing to the ocean, causing water mass to shift outward from the Earth's rotational axis—akin to extending arms in a spinning chair. Thus, large dams indeed impact Earth's spin!

Let's delve into the effect of the Three Gorges Dam. As this construction holds a significant water mass, positioned geographically away from Earth's axis, this affects the planet's angular velocity and consequently lengthens the day.

Calculating this change using specific parameters like latitude, water mass, and depth reveals the rate of Earth's rotation alters slightly—adding approximately 5.3 microseconds to a day. Although negligible, this demonstrates human constructions' potential to influence planetary dynamics.

Hypothetically, stacking more water structures or adjusting mass distributions could further extend the length of a day. Just by standing up en masse, humans could hypothetically affect Earth's rotation slightly!