Problem about uniform thin disk

In summary, a uniform thin disk is a flat, circular physical system with a uniform mass distribution used to simplify complex systems in physics and engineering. It has various applications in fields such as astronomy, mechanics, and engineering. The moment of inertia for a uniform thin disk can be calculated using a specific formula. Its main difference from a solid disk is its uniform mass distribution. A uniform thin disk cannot have a non-uniform thickness.
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Why do they only think of kinetic energy of motion?
Why don't they think of both kinetic of motion and kinetic of rolling energy?

So. i think
## L = \frac{1}{2}mv^2 + \frac{1}{2}I \omega^2##
## L = \frac{1}{2}m(r \omega)^2 + \frac{1}{2}(\frac{1}{2}mr^2) \omega^2##
## L = \frac{3}{4} mr^2 \omega^2##
 
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  • #2
Look at the last three equations in the answer. The result will be the same whether you multiply ##mr^2\omega^2## by ##\frac{3}{4}## or ##\frac{1}{2}##. It looks like whoever wrote the solution knew the bottom line and became sloppy.
 
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Related to Problem about uniform thin disk

1. What is a uniform thin disk?

A uniform thin disk is a type of physical system that is characterized by a circular shape and a constant thickness throughout its entire structure. It is often used as a simplified model for studying the behavior of objects such as planets, stars, and galaxies.

2. What are some common problems associated with uniform thin disks?

Some common problems associated with uniform thin disks include understanding their stability, rotation, and gravitational interactions with other objects. These problems can be challenging to solve due to the complex nature of the disk's structure and the various forces acting upon it.

3. How are uniform thin disks used in scientific research?

Uniform thin disks are used in scientific research to model and simulate the behavior of various objects in space, such as galaxies and planetary systems. They are also used in engineering and material science to study the properties and behavior of thin circular structures.

4. What are some real-world applications of uniform thin disks?

Uniform thin disks have several real-world applications, including in the design and construction of mechanical components such as gears and bearings. They are also used in the production of computer hard drives, which rely on the rotation and stability of thin disks to store and retrieve data.

5. What are the limitations of using a uniform thin disk as a model?

One of the main limitations of using a uniform thin disk as a model is that it does not accurately represent the complex and irregular shapes of many objects in the real world. Additionally, it may not account for all the forces and interactions that occur in a non-uniform disk, leading to less accurate predictions and results.

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