Ask a Physicist Answers

Why is it said that increasing heights of building affect the revolution time of earth?

That is an interesting question. While I’ve never heard anyone say that to me, let’s see why someone might make such a statement

Consider an ice skater spinning around. When the ice skater sticks out her hands, she spins slower. Then she rotates really fast when she pulls her arms to her sides. This is an example of a fundamental law in physics called Conservation of Angular Momentum. This law relates two observable quantities: the speed of rotation and the shape. Essentially this law says that the speed of the spinning object times the shape of the object is always the same amount. Since these qualities put together are always the same, then that means if one decreases then the other must compensate by increasing. Let’s see how this works: when I mentioned that the ice skater decreases her shape by pulling her arms to her sides, her rotational velocity increased. When two quantities are oppositely related in this way, we say that they are inversely proportional. When one goes up then other goes down and vice versa –like a balance scale.

How do we describe the shape of an object? This quantity needs to describe how the mass of a spinning object is distributed. The mass in the skater’s arms have the property of inertia which resists changes in motion. Inertia also contributes to the momentum of a moving object. Faster moving objects have greater momentum than slower objects. When the skater’s arms are outstretched, they are moving faster. As a result, her arms have greater momentum than when they are pulled close to her body. This means that a rotating object with outstretched arms will have more momentum and will also be more resistant to any outside changes in its rotation. Try spinning a friend on a rotating chair. You will find that it is harder to stop their motion when their arms our stretched as opposed to folded. We will call this phenomenon moment of inertia. For symmetric objects like balls and cylinders, the moment of inertia is easy to calculate. For more awkward objects like an ice skater, it requires more math. However, the moment of inertia is typically proportional to the mass of an object times its radius squared. Most physics textbooks have a table with formulas for the moment of inertia of simple objects.

Now let’s consider the case of when the skater spreads her arms out. This means that she changes her shape and increases her moment of inertia. Conservation of angular momentum tells us that this increase in moment of inertia must cause a decrease in rotational velocity. And as a result we see her spinning much slower with her arms stretched out.

Now what in the world does this have to do with the question, you might demand. Can you see any similarity between the ice skater and the rotating earth? They both spin in cold environments and they can both change their shape. Just as the ice skater can spread out her arms, the earth can form mountains and with the help of humans construct skyscrapers.  These protrusions increase the moment of inertia of the Earth which according to conservation of angular momentum should slow the Earth’s rotation.

Don’t panic! Let’s put this in perspective. Imagine that we could construct solid skyscrapers that were all three times the height of the Empire State building and we built one on every spot on the planet. In other words, the Earth would look like one giant city that is taller than any city we have ever seen. In this case, the buildings would cause the earth to slow and as a result the length of the day would increase by 27 seconds. However, we don’t have gigantic cities like this all over the planet. The actual effect of our city skyscrapers on the rotation of the Earth is much less than the tidal effects of the moon which extends the day about 0.0016 seconds every century.

This is great example of a physics thought experiment which is often referred to as theoretical physics. In a thought experiment you can deduce a valid conclusion that won’t necessarily occur when you calculate the actual numbers. These calculations often yield results that are ridiculously small. Like 0.0000000000….until your eyes cross.

Another simple example of this has to do with Newton’s law of gravity which suggests that you should feel an attractive force pulling you towards your classmates. However, this force is so ridiculously small that you would sooner feel the flutter of a butterfly in China. If you are attracted to one of your classmates, you can be sure it’s not gravity.