Why doesn’t the Pisa tower topple?

Unless you have been living under a rock your whole life, you must have heard of the Leaning tower of Pisa. Situated in Pisa town of Italy, the tower was constructed between 12th and 14th century AD. The tower was meant as the freestanding bell tower of Pisa Cathedral, and was most certainly not designed to be a leaning one! The leaning is a result of the unstable foundation of the building, which is said to be built on unsettled soil. But even after 800 years, it still stands. Why? To answer this question, we need to have a look at a physics concept named “Center of Mass”.

The leaning tower of Pisa
How much do you weigh? Say you weigh 60 Kg (Measuring weight in Kilograms is wrong, but that is a completely different topic). Where is this weight exactly? It is distributed all over your body. Each of your hands may weigh around 5 Kgs, and your head may be around 3 Kgs. Unless you are a sumo wrestler (or a local politician), your stomach might not exceed 10 Kgs, and the list goes on. But if we consider all these weights into a one point of your body, where would it be? Due to symmetry of our body, and the way we are built, this point would lie inside your stomach, slightly above your naval. This is only true if you are standing still, as you can understand, any movement of your body parts can shift this point elsewhere (though not very far). This point where we can consider all our weight to be concentrated is called the “Center of Mass” in Physics. All physical objects have one, and the gravity always pull the object to the ground from this point. For this reason, the point is also known as “Center of Gravity”.

One of these should fall, which one?
Now, for an object to remain upright (not to topple over), the perpendicular drawn from this “Center of Mass” should fall inside its base. Feeling confused? Look at above image. The image shows two cylinders, and both cylinders have perpendiculars drawn from their center of masses. This line falls within the base of the first cylinder, so it should remain upright. The second cylinder must fall, as its line falls outside the base. This is true, even for us. Don’t believe me? Try bending front, while keeping your feet closer. As soon as your center of mass leaves your base, you will fall over. Now you can understand why tall objects with smaller bases (eg- a bookshelf) tend to fall over far easily than shorter objects with wider bases (eg- a table). Believe it or not, you have been using this principal your whole life, without you knowing it! Whenever riding a bus while standing, why do you place your legs apart? When placing a book on a table, why don’t you keep it upright? In fact, let me challenge you to prove my point.

Image courtesy - Physics for Entertainment by Y. Perelman (a must read for all physics lovers)
Take a normal chair (without arm rests), and sit as shown in the image. Now try to stand. The only conditions are, you cannot pull your legs back, and you cannot bend forward. You will see that it is impossible! This is because, when sitting, your center of mass falls within the base of the chair. But when you stand up, it should fall within your leg base. To achieve this, you either have to bend forward, or move your legs back. You have been doing this your whole life, without you knowing it! Physics is fascinating, isn’t it?

OK, back to leaning tower. If you observe carefully, you can see that its center of mass lies within its base. So it does not topple over. This is the main reason for it to remain upright. Another reason is it having a deeper base. Also, over the years, some renovations have been done to the tower, to shift its center of mass from its original location towards the outer wall. Due to all these reasons, the tower of Pisa still remains upright, and hopefully will remain so for a long time to come. Now that you know why it doesn’t fall, and what center of gravity is, let me ask you a different question. Look at the below image. Clearly, his center of mass lies outside of its base. So why doesn’t he fall over? Leave your answer in the comments section, and stand a chance to win a price!!
Why doesn't this biker fall?

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