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

[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?

 

[eljose79]

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!