Conservation of angular momentum book problem

In summary, the conversation is about calculating the initial angular momentum of a disk with a reference point at B. The solution involves including the angular momentum of the rod, disk, and their respective centers of gravity. The velocity of the rod's center of gravity is not included because it has already been taken into account through the use of the Parallel-Axis Theorem. This is due to the moment of inertia used for the rod being 1/3ML2. If the MOI used was 1/12ML2, then the angular momentum contribution from the velocity of the rod's center of mass would need to be added. This clarification was provided by Jeremy.
  • #1
joahe
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Homework Statement


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2. The attempt at a solution

I set the initial angular momentum of the disk = to the sum of : rod's angular momentum, angular momentum of disk, rod's center of gravity and disk's center of gravity. With the reference point being at B.

Why is the velocity of the rod's center of gravity not included in the solution?

Thanks for any and all help.
 
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  • #2
joahe said:
Why is the velocity of the rod's center of gravity not included in the solution?

It has already been taken into account because the moment of inertia used for the rod was 1/3ML2. If the MOI used was 1/12ML2 then you can add the angular momentum contribution from the velocity of the rod's center of mass. This is essentially the application of the Parallel-Axis Theorem.

Hope this helps!
 
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  • #3
JeremyG said:
It has already been taken into account because the moment of inertia used for the rod was 1/3ML2. If the MOI used was 1/12ML2 then you can add the angular momentum contribution from the velocity of the rod's center of mass. This is essentially the application of the Parallel-Axis Theorem.

Hope this helps!

Thanks Jeremy, that completely clears things up. Cheers!
 

FAQ: Conservation of angular momentum book problem

What is the conservation of angular momentum?

The conservation of angular momentum is a fundamental law of physics that states that the total angular momentum of a system remains constant unless an external torque is applied. It is a result of the principle of conservation of energy and is applicable to both classical and quantum mechanics.

How is angular momentum conserved in a book problem?

In a book problem, angular momentum is conserved by the book's rotation around its center of mass. As long as there are no external torques acting on the book, the angular momentum remains constant, even as the book's shape or orientation changes.

What are the factors that affect the conservation of angular momentum in a book problem?

The conservation of angular momentum in a book problem is affected by the mass, velocity, and distance from the center of mass of the book. The distribution of mass and the shape of the book also play a role in determining the angular momentum.

Can angular momentum be transferred between objects in a book problem?

Yes, angular momentum can be transferred between objects in a book problem. For example, if one part of the book rotates faster, the other parts will rotate slower to conserve the total angular momentum of the system.

How is the conservation of angular momentum applied in real-life situations?

The conservation of angular momentum has many practical applications in real-life situations. For example, it is used to explain the stability of objects such as spinning tops, gyroscopes, and satellites. It is also essential in understanding the motion of celestial bodies, such as planets and stars.

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