Application of integrals to find moment Inertia

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The discussion focuses on integrating physics and mathematics by using integrals to calculate moment inertia of areas for a project. The original poster is considering creating a small windmill or fan blades but questions their appropriateness since the theory primarily applies to 2D objects. Suggestions for simpler projects that utilize integrals in physics are also requested. A participant notes that symmetrical objects can simplify the application of the theory, potentially broadening project options. Clarification is sought on these concepts, indicating some confusion about the application of the theory.
Kumaken
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I need to make a project that integrates physics with math, involving the use of integrals to find moment inertia of areas. The theory could be read here :http://www.intmath.com/applications-integration/6-moments-inertia.php

I need to make an object that applies the theory above. Can anybody recommend me what should I make?

*note : I have a few idea in mind like making small windmill or fan blades that rotate, but are they appropriate? Cause I think the theory only applies to 2D objects...

*another note : If it's too much hassle, what project do you think is simple that involves the application of integrals in physics? Thank you very much in advance.
 
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For anything that is symmetric above with below a plane will be like you concentrated all the mass that has coordinates x, y into the xy plane, maybe that extends your possibilities.
 
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epenguin said:
For anything that is symmetric above with below a plane will be like you concentrated all the mass that has coordinates x, y into the xy plane, maybe that extends your possibilities.
I'm sorry but I kinda do not understand... can you please elaborate? Sorry for the trouble.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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