One of Carrillo's pirouettes during the figure skating final.

One of Carrillo's pirouettes during the figure skating final.
One of Carrillo’s pirouettes during the figure skating final.ALEKSANDRA SZMIGIEL (REUTERS)

To explain what angular momentum is, I am going to relate it to linear momentum because most of us are much more used to thinking about it. If we want to characterize the motion of a body, we need two quantities: mass and speed. It is easy to understand it intuitively: it is not the same as something very light, a leaf from a tree, moving towards us, as something very heavy, a brick. And similarly, if those two objects are moving towards us, we are interested in whether they are moving fast or slow. So we can understand that we need both magnitudes to measure that amount of linear momentum. When something rotates, when it has a rotational movement about an axis or a reference point, we use angular momentum instead of linear momentum that I just talked about.

That is, angular momentum about a point characterizes the motion of something that rotates around that same point. In this case, the two magnitudes that we need to measure it are the moment of inertia (which in the linear is the mass) and the angular velocity (which in the linear is the linear speed).

Angular momentum is not an intrinsic property of a body. The mass, for example, yes it is, each body has its mass. Angular momentum is always defined with respect to a point that will be the center of rotation. Therefore, an object can have a certain angular momentum with respect to one point, but not have it with respect to another. Logically, only when it rotates and always with respect to the point of rotation. It’s like speed, something is moving or not, with respect to what we measure it. If I drive a car with a passenger, someone who sees us pass sees how my passenger moves, but for me he is not moving because he is sitting next to me.

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Another interesting fact about angular momentum is that it is conserved, that is, the angular momentum of a body with respect to a point will not change unless an external force is applied. And not just any force, it has to be one that changes the state of rotation of the object.

We can think of two cases with two types of forces, one that does not change the angular momentum and one that does. For example, in a planetary system the planets revolve around a point and have an angular momentum that will remain mostly constant. This is true because the force of gravity acting on them is central, so their speed of rotation around that central point does not change. For the second case, if we think of a spinning bicycle wheel and we want to make it spin faster, we are going to drive it tangentially (and not towards the center of the wheel, which is where the axis of rotation is). Since angular momentum is calculated as the product of moment of inertia and angular velocity, we see that by changing the rate of rotation with a tangential force we are also changing the angular momentum of the wheel.

Finally, we are left to talk about the moment of inertia. This quantity tells us for a certain body how all the parts that compose it are distributed with respect to an axis of rotation. That is, whether the mass of the spinning object is near or far from the axis. The greater the distance to the axis of rotation, the greater the corresponding moment of inertia. Like angular momentum, it is not something intrinsic, and it is that the moment of inertia of a body will change if its shape changes or if we change the axis of rotation.

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There is an example that serves to illustrate it and it is figure skating. In this sport we see how by changing the position of the body, if a part of the body approaches or moves away from the center of rotation during a pirouette, the speed of the athlete’s rotation changes. What we are seeing is that its angular momentum remains constant during the spin because the total effect of external forces is so small that we can ignore it. Since angular momentum is the product of those two quantities I was talking about, moment of inertia and angular velocity, if one decreases, the other has to increase. By bringing arms and legs closer to the axis of rotation, the moment of inertia decreases, so the speed of rotation has to increase for the product of the two, that is, the angular momentum, to remain constant.

Maria Vieites Diaz She is a doctor in Particle Physics and a researcher at the High Energy Physics Laboratory of the Federal Polytechnic School of Lausanne (Switzerland).

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