Angular momentum extended body

In summary, the conversation discusses calculating the angular momentum of a system with two slender rods colliding. The speaker is unsure of how to calculate this, as the formula L=Iw does not seem applicable. The other person explains that the total angular momentum can be divided into the motion of the center of mass and the motion about the center of mass. They suggest using the center of mass as the origin for calculating angular momentum and transforming the diagram to a frame where the center of mass is at rest. This simplifies the calculation since neither rod is initially rotating.
  • #1
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Suppose I have the system on the attached file, where two slender rods collide. I want to calculate the angular momentum of the system before collision relative to the center of mass of the two rods. I'm however not sure how to do this. Definately the formula L=Iw doesn't apply, since I don't know from which point I should measure the angular velocity. Equivalently I don't know where what R to use if I use the formula: L = mvR. It seems intuitive if it was the center of mass, but why it is, I have no idea. Who can explain what R to use and why?
 

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  • #2
You can always treat the total angular momentum of a system as composed of the angular momentum due to the motion of its center of mass plus the angular momentum about its center of mass.

If you wish to use the center of mass as your origin for computing angular momentum, just transform your first diagram to a frame in which the center of mass is at rest. Since neither rod is rotating (at first), all you have to worry about is the motion of each rod's center of mass.
 

What is angular momentum extended body?

Angular momentum extended body refers to the rotational motion of an object around an axis. It takes into account not only the mass and velocity of the object but also the distribution of its mass around the axis of rotation.

What is the formula for calculating angular momentum extended body?

The formula for calculating angular momentum extended body is L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

How is angular momentum extended body related to conservation of angular momentum?

Angular momentum extended body is related to conservation of angular momentum in that the total angular momentum of a system remains constant in the absence of external torques. This means that if one part of the extended body experiences a change in angular momentum, another part of the body will experience an equal and opposite change in order to maintain the total angular momentum of the system.

What is moment of inertia?

Moment of inertia is a measure of an object's resistance to rotational motion. It takes into account the mass and distribution of the mass around an axis of rotation.

How does the shape of an object affect its moment of inertia and angular momentum extended body?

The shape of an object can greatly affect its moment of inertia and angular momentum extended body. Objects with a larger moment of inertia, such as a long rod, will have a greater resistance to rotational motion and therefore a larger angular momentum. Objects with a smaller moment of inertia, such as a sphere, will have a lower resistance to rotational motion and therefore a smaller angular momentum.

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