# Why Does Angular Momentum Differ from Other Angular Relationships in Physics?

• UR_Correct
In summary, angular momentum is a measure of an object's rotational motion and is calculated by multiplying its moment of inertia by its angular velocity. In a closed system, the total angular momentum remains constant due to the law of conservation of angular momentum. The distribution of mass affects an object's angular momentum through its moment of inertia. Angular momentum differs from linear momentum, which is a measure of linear motion. In space, the law of conservation of angular momentum is crucial in explaining the motion of objects, as there are no external forces to slow down or stop rotational motion.
UR_Correct
Hello all!

I'm currently studying for a physics exam in regards to Newtonian mechanics. This chapter is about angular momentum, moments of inertia, etc.

As I was studying, something dawned on me, and I wondered if someone here might be able to help me.

The following relations are apparent to me:

velocity = radius * angular velocity
acceleration = radius * angular acceleration

But,

angular momentum = radius * momentum

Why is this? I, for some reason, assumed it would keep with the pattern for position, velocity, and acceleration and their respective angular relations.

I'm thinking it has to do with the fact that, when dealing with vectors, you have to take radius cross momentum. I know that the angular momentum vector points perpendicular from the direction of momentum (right hand rule), but I can't come up with a definitive answer.

Can anybody shed any light?

Hello there!

You are correct in your assumption that the relation for angular momentum is different from the other angular relations. This is because angular momentum is a vector quantity, while velocity, acceleration, and position are all scalar quantities.

In order to fully understand the relationship between angular momentum and its counterparts, we need to first define what angular momentum is. Angular momentum is the measure of an object's rotational motion, and it is calculated by multiplying the object's moment of inertia (a measure of its resistance to rotational motion) by its angular velocity. This gives us a vector quantity that points in the direction of the axis of rotation.

On the other hand, momentum is a measure of an object's linear motion, and it is calculated by multiplying its mass by its velocity. This gives us a vector quantity that points in the direction of its motion.

As you mentioned, to find the angular momentum vector, we need to take the cross product of the radius vector (from the axis of rotation to the point of interest) and the momentum vector. This results in a vector that is perpendicular to both the radius and momentum vectors, pointing in the direction of the axis of rotation.

In contrast, to find the velocity and acceleration vectors, we simply need to take the derivative of the position and velocity vectors, respectively. This does not involve any cross products, as they are scalar quantities.

So, in summary, the difference in the relationships between angular momentum and its counterparts is due to the fact that they are different types of quantities (vector vs. scalar) and they are calculated using different methods. I hope this helps to clarify things for you. Good luck on your exam!

## 1. What is angular momentum and how is it related to rotational motion?

Angular momentum is a measure of the rotational motion of an object. It is the product of an object's moment of inertia and its angular velocity. In simpler terms, it is the tendency of an object to keep rotating at a constant speed.

## 2. How is angular momentum conserved in a closed system?

In a closed system, the total angular momentum remains constant. This means that if one object in the system increases its angular momentum, another object must decrease its angular momentum by an equal amount. This is known as the law of conservation of angular momentum.

## 3. How does the distribution of mass affect an object's angular momentum?

The moment of inertia, which is a component of angular momentum, is directly influenced by an object's distribution of mass. Objects with more mass concentrated towards the center have a lower moment of inertia and therefore a higher angular momentum. Objects with more mass distributed further from the center have a higher moment of inertia and a lower angular momentum.

## 4. What is the difference between angular momentum and linear momentum?

Angular momentum is a measure of rotational motion, while linear momentum is a measure of linear motion. Linear momentum is the product of an object's mass and its linear velocity, while angular momentum is the product of an object's moment of inertia and its angular velocity.

## 5. How can angular momentum be used to explain the motion of objects in space?

In space, there is no friction or external forces to slow down or stop an object's rotational motion. As a result, the law of conservation of angular momentum plays a crucial role in explaining the motion of objects in space. For example, when a spinning object in space contracts, its moment of inertia decreases, causing an increase in its angular velocity to maintain a constant angular momentum.

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