Finding Center of Mass and Moment of Inertia for a Hemispherical Shell

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SUMMARY

The discussion focuses on calculating the center of mass and moment of inertia for a thin hemispherical shell with radius R and mass M, centered at the origin. Participants emphasize the importance of attempting the problem independently before seeking help, highlighting that mathematics requires perseverance and effort. The conversation also addresses the common tendency of users to seek immediate solutions without prior attempts, which can lead to unconstructive responses from the community.

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  • Understanding of basic physics concepts such as center of mass and moment of inertia.
  • Familiarity with the geometry of hemispherical shells.
  • Knowledge of integral calculus for solving physics problems.
  • Experience with mathematical problem-solving techniques.
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  • Study the derivation of the moment of inertia for different geometric shapes, including hemispherical shells.
  • Learn about the application of integral calculus in physics problems, particularly in finding centers of mass.
  • Explore examples of similar physics problems to practice and reinforce understanding.
  • Investigate common pitfalls in mathematical problem-solving and strategies to overcome them.
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Students in physics or engineering courses, educators teaching mechanics, and anyone interested in understanding the principles of rotational dynamics and geometry.

jlmac2001
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Find the position of the cnter of mass and moment of inertia for rotations about an axis through the origin and along axis of symmtry of a thin hemisphericl shell of radius R and mass M whose center is at the orgin.

For this problem, would I treat is kinda like a sphere? How would I do something like this?
 
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If you keep posting every question you're set in this course you're going you're going to get some nastier responses than this.

There have been several responses showing you how to find moments of inertia; perhaps it's time you solved this one on your own? You have the formulae, you've seen the examples, show us what you've done so far.
 
sorry

If I knew how to do it, i would not have posted. Thanks anyway.
 
lots of people post without actually attempting to solve the problem first. Maths problems aren't supposed to be easy, and once you're onto sufficiently hard material then it should take you quite a while to solve the problems. don't give up instantly, which is what most people do when they don't see the solution immediately. that isn't how maths really works.

there seems to have been a spate of people posting messages that read 'for god's sake don't be so lazy/stupid', but slightly more confrontationally, recently, so I thought I'd warn you you might get some answers you didn't want.

so, how do you think you do the question? where would you start, where do you get stuck?

matt
 

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