Ratio H/R to in tensor problem, just making sure i did this right

In summary, the H/R ratio is a measurement used to describe the shape of an object in tensor problems. It is calculated by dividing the height by the radius of the object. A common H/R ratio in these problems is 1, indicating a spherical shape. This ratio can impact an object's physical properties, such as its surface area, strength, and stability. It is a useful tool in many fields, including engineering, physics, and materials science.
  • #1
m0nk3y
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[SOLVED] ratio H/R to in tensor problem, just making sure i did this right

Homework Statement


What is the ratio of height to radius that you need such that all the diagonal elements of the inertia tensor along its diagonal are equal?


Homework Equations





The Attempt at a Solution



http://scienceworld.wolfram.com/physics/mimg276.gif
Since my Ixx=Iyy i made one of them = to Izz, i did some simple algebra and got h/R = sqrt(3) is this right? If not where did I go wrong?

Thanks
 
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  • #2
You are correct.
 
  • #3
Yes! Thank you.
 

Related to Ratio H/R to in tensor problem, just making sure i did this right

What is the purpose of using the H/R ratio in a tensor problem?

The H/R ratio, also known as the height-to-radius ratio, is used to describe the shape of an object. In tensor problems, it is used to determine the relationship between the dimensions of an object and its physical properties.

How do you calculate the H/R ratio in a tensor problem?

To calculate the H/R ratio, you need to measure the height and radius of the object. Then, divide the height by the radius to get the ratio. For example, if an object has a height of 10 cm and a radius of 5 cm, the H/R ratio would be 2 (10 cm / 5 cm = 2).

What is a common H/R ratio in tensor problems?

The H/R ratio can vary greatly depending on the object being studied. However, a common H/R ratio in tensor problems is 1, which indicates a spherical shape. Objects with a higher H/R ratio may have a more elongated shape, while objects with a lower H/R ratio may be more flattened.

How does the H/R ratio affect the properties of an object in a tensor problem?

The H/R ratio can affect the physical properties of an object in a tensor problem by influencing its shape and dimensions. For example, an object with a higher H/R ratio may have a greater surface area and therefore may experience more friction when moving through a fluid. Additionally, the H/R ratio can also impact an object's strength and stability.

Can the H/R ratio be used in any type of tensor problem?

Yes, the H/R ratio can be used in a wide range of tensor problems, as long as the object being studied has a defined height and radius. It is commonly used in engineering, physics, and materials science to analyze the structural properties of various objects.

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