How is τmax/rmax related to the second moment of area?

  • Thread starter Riazy
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In summary, "Τmax/rmax Inegrating r^2 dA" is a calculation that involves determining the maximum torque divided by the maximum radius while integrating the area of a shape raised to the power of 2. This calculation is important in scientific research because it provides information on the maximum torque that can be exerted on an object while considering its surface area distribution. It is different from other torque calculations as it takes into account the distribution of surface area. This calculation can be applied to any shape with a defined surface area, but the shape must be symmetrical. Some potential real-world applications of "Τmax/rmax Inegrating r^2 dA" include analyzing the structural stability of buildings, determining the strength
  • #1
Riazy
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Homework Statement



dT= τmax/rmax * r^2 dA

T = τmax/rmax ∫▒〖r^2 dA〗

as far as I am concerned integrating this will give us r^3/3 + c?
or am i thinking wrong, how did my teacher get the answer below in bold

Homework Equations


its not a great deal to do but I don't know how my professor got the following answer below


The Attempt at a Solution


the question is why the answer to this is

τ/rmax * Ip
 
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  • #2
The second moment of area is defined as

[tex]I = \int_A r^2 dA[/tex]


had you ∫r2 dr, then you'd get r3/3 + C
 

1. What is "Τmax/rmax Inegrating r^2 dA" in scientific terms?

"Τmax/rmax Inegrating r^2 dA" refers to the calculation of the maximum torque (Τmax) divided by the maximum radius (rmax) while integrating the area (dA) of a shape raised to the power of 2.

2. Why is "Τmax/rmax Inegrating r^2 dA" important in scientific research?

This calculation is important because it allows scientists to determine the maximum torque that can be exerted on an object while considering the distribution of its surface area. This information can be useful in studying the structural integrity and stability of various objects, such as bridges or buildings.

3. How is "Τmax/rmax Inegrating r^2 dA" different from other torque calculations?

Unlike other torque calculations that only consider the force and distance from the pivot point, "Τmax/rmax Inegrating r^2 dA" takes into account the distribution of surface area, providing a more comprehensive analysis of torque.

4. Can "Τmax/rmax Inegrating r^2 dA" be applied to any shape?

Yes, this calculation can be applied to any shape with a defined surface area. However, the shape must be symmetrical in order to accurately determine the maximum torque using this method.

5. What are some potential real-world applications of "Τmax/rmax Inegrating r^2 dA"?

"Τmax/rmax Inegrating r^2 dA" can be used in a variety of fields, such as engineering, architecture, and physics. It can be applied to analyze the structural stability of buildings, determine the strength of various materials, and even calculate the force needed to turn objects, such as screws or bolts.

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