# About an example related to angular momentum in a textbook

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In summary, the conversation discusses the relationship between angular velocity and angular momentum vectors, specifically how they generally have different directions. The example given involves two point masses connected by a rigid bar, showing how their angular momentum vectors are in the same direction but their angular velocity vectors are not. This illustrates why the two vectors are usually not parallel.
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Hey I either have the worst physics textbook in the history of physics textbooks or i can't understand a topic.I'd appreciate if you help me decide which is it.
(Pic related is the image of the example)
First let's agree on the symbols let's call angular velocity: $\omega = \frac{rxv}{||r||^2}$ , angular momentum $L=rxmv$ and Lineal Momentum:$P=mv$. Being that defined, the book attemps to proof that $L$ and $$\displaystyle \omega$$ have generally different directions, here is the first problem i encountered, for what i know $m||r||^2\omega = L$ being $m||r||^2$ That means that Angular Velocity and Angular Momentum are parallel therefore have the same direction, the example proceed as following: 2 puntual mass are united by a rigid bar of despicable mass, therefore both have the same angular momentum. the momentum of body 1 is $L_1 = r_1xm_1v_1$ and it explicitly say that it's easy to see that it's contained in the plane given by $P_1 P_2 \omega$ (which i fail to see) being the direction perpendiculat to the line that unites $P_1$ with $P_2$ and that $L_2$ Has the same direction that $L_1$. Therefore the Angular Impulse make an angle of $\frac{\pi}{2}-\alpha$ with the axis of rotation($\omega$). Well that'd be an example i'd really appreciate if someone can clarify my doubts, i don't have a teacher to ask since i study by my own.
Here is a picture of the example:

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It looks like your textbook is trying to explain why the angular momentum and angular velocity vectors are usually not in the same direction. The angular momentum vector is a vector that points from the point mass to the axis of rotation, and its magnitude is the product of the mass and the distance from the axis of rotation times the velocity. The angular velocity vector points along the axis of rotation, and its magnitude is the product of the radius and the velocity.In the example, they explain how if two point masses are connected by a rigid bar, then the angular momentum vector of each point mass will be in the same direction, but the angular velocity vector will not be in the same direction. This is because the angular velocity vector is always perpendicular to the line connecting the two point masses, and the angular momentum vector is always in the plane defined by the two point masses and the angular velocity vector.This example should make it clear why the angular momentum and angular velocity vectors usually do not have the same direction. Hope this helps!

## 1. What is angular momentum?

Angular momentum is a physical quantity that describes the rotation or spinning motion of an object. It is the product of an object's mass, velocity, and distance from a fixed point or axis of rotation.

## 2. How is angular momentum represented mathematically?

Angular momentum is represented by the symbol L and is calculated by multiplying an object's moment of inertia (I) by its angular velocity (ω). The formula for angular momentum is L = Iω.

## 3. Can you provide an example of angular momentum in a textbook?

A common example of angular momentum in a textbook is a spinning top. As the top spins, it has angular momentum that keeps it upright even when it starts to wobble. The faster the top spins, the greater its angular momentum.

## 4. How is angular momentum related to conservation laws?

Angular momentum is a conserved quantity, meaning that it cannot be created or destroyed. This is known as the law of conservation of angular momentum. In a closed system, the total angular momentum remains constant, even if individual objects within the system may experience changes in their angular momentum.

## 5. How is angular momentum used in real-world applications?

Angular momentum has many practical applications in fields such as physics, engineering, and astronomy. It is used to study the motion of celestial bodies, design vehicles and machines that rotate, and analyze the behavior of spinning particles at the atomic level.

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