While studying, we often don't realize the value of what we're learning. I recently had a surprising experience with modern bowling balls. I'm not a big bowler, far from it, as that would contradict the stereotype of a theoretical physicist. Instead, I was intrigued by the inner values: of the bowling balls, not the physicist. While doing research on them, I discovered some connections from my studies that I want to share with you.
About rotating bodies
Rotating, extended bodies are one of the most confusing topics you come across when studying physics, so that you are glad when you no longer have much to do with them. You have to deal with forces that are not actually forces (centrifugal and Coriolis force), and as soon as the body no longer rotates around its centre of gravity, things become even more complicated. Nevertheless, let's get to the bottom of the matter. A very important property of rotating bodies is the moment of inertia, which is a quantity that describes how easily an object can be set into rotation. The greater the moment of inertia, the more energy must be employed to set the body in rotation. However, it is not only the mass but also its distribution that plays an important role.
Let's think of a gyroscope that is set into rotation. The axis of rotation of a symmetrical body normally lies along the axis of symmetry - a vertical line along its centre. If there were no other forces acting on the body apart from the rotational force and if there were no air resistance and no gravitational force, the body would (theoretically!) rotate forever. However, as this is not the case in reality, additional forces act on a rotating body in the form of a torque, and so the axis of rotation begins to move to the side. This phenomenon is known as precession and causes the axis of rotation form a cone. If an additional force acts on the axis of rotation, it begins to wobble. An effect known as nutation. A graphical representation of rotation, precession and nutation can be seen in the picture above.
For nonsymmetrical objects, like a potato, things become more complicated, because there is more than one rotation axis. If you rotate these objects, it depends on which axis and at what speed this happens. If you get the axes with the largest or smallest moment of inertia, you are lucky because they are characterised by stable movement. However, if the axis of rotation lies in between, you have nutation. If you want to understand these movements in more detail, you cannot avoid the so-called Euler equations. A system of three coupled, non-linear differential equations! Sounds beautiful, right?
On bowling balls, astrology and modern medicine
For all those who have made it this far: what does this have to do with bowling balls? Contrary to my naive assumption, these monsters are not just heavy, round and have three holes. Actually, the professional versions are quite something. They are fitted with bulky weights on the inside. This does not only compensate for the asymmetry created by drilling the holes for the three fingers, but this allows expert bowlers to shamelessly exploit the aforementioned effects such as moment of inertia, nutation and precession. Understanding these effects is one thing, but being able to use them in everyday life is a real challenge!
Professional bowlers do not try to hit the pins at the end of the lane in a straight line. Instead, they aim for a curved path, ideally hitting the target at a 6-degree angle from the side. Bowling balls with a small moment of inertia can be rotated more quickly with the same effort. In the first 2/3 of the lane, which is oiled, the ball glides while rapidly rotating. In the back part, the movement changes into a rolling motion, and the ball makes a hook. Nutation and precession are then used to minimize the amount of oil between the ball and the lane in the hook phase, making the hook stronger. If a bowling ball is thrown correctly, you'll find a sequence of streaks traveling along the ball, known as track flares, which is not possible with a regular ball! This becomes nicely visible in a video, in which I had the chance to participate in.
Another asymmetrical ball that plays an important role in our lives is the Earth. While some still argue whether it's round or flat, as a physicist, I must say it's more like a slightly flattened potato. Similar to the bowling ball, this uneven mass distribution causes nutation, which is translated into a wobbling of the Earth's axis. This has several periods, with the shorter one (approximately 14 months) discovered by the American Seth Carlo Chandler. The measurement of the longer period (approximately 18.6 years) was accomplished by the British astronomer James Bradley in the 18th century. Additionally, the Earth is influenced by the Sun, Moon, and other planets, causing a precession movement. Although this effect is the strongest, it has the longest period. The Earth's axis returns to the same position only every 25,800 years. Currently, it points quite precisely towards the North Star.
This strong rotation also changes the apparent positions of all celestial bodies, including the zodiac signs. The ancient Greeks already noticed this by comparing old star maps. The constellations where the Sun resides in corresponding months shift about one position every 2000 years. This results in the zodiac signs we attribute to ourselves having nothing to do with today's celestial mechanics. If you've been seeking love advice in the Taurus section of your horoscope, it might be better to consult Aries or just skip to the science section!
For those who don't want to rely on a horoscope to know a person's inner qualities, the best option is to go for a Magnetic Resonance Imaging (MRI) scan. This imaging technique, indispensable in modern medicine, relies on a similar effect as our bowling pros. The so-called spin of hydrogen nuclei in human tissue can be thought of as a rotation axis. By applying strong magnetic fields, all rotation axes are aligned. An additional applied high-frequency field then causes the nuclear spins to precess. When the high-frequency field is turned off, the spins slowly return to their original position. By measuring this relaxation time, this means the time it takes for the spins to return to their original position, conclusions can be drawn about the type of surrounding tissue. Simply put: this takes longer, for example, in tumor tissue than in muscle tissue, making it clearly visible in the MRI image. The functioning of an MRI is, of course, much more complex in reality, but the principle has more in common with holey, colorful balls than one might initially believe! (Dominik Kreil, 7.5.2024)