- #1
PSOA
Why is the end area of shell [tex]2\pi rdr[/tex]?
Thanks in advance.
Why is the End Area of Shell 2πrdr in the Moment of Inertia Formula?
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Homework Help Overview
The discussion revolves around understanding why the end area of a cylindrical shell is represented as 2πrdr in the context of the moment of inertia formula. The topic is situated within the realm of calculus and physics, particularly focusing on integration and differential areas.
Discussion Character
- Conceptual clarification, Mathematical reasoning
Approaches and Questions Raised
- Participants explore the meaning of the differential area 2πrdr, with one participant explaining that it represents an infinitesimal area derived from the circumference and thickness of the shell. Others express their initial understanding of integration and its application in this context.
Discussion Status
The discussion is active, with participants engaging in clarifying the concept of differential areas and integration. One participant acknowledges understanding the explanation provided, indicating a productive exchange of ideas, though no consensus on the broader implications of the moment of inertia is reached.
Contextual Notes
Participants mention the learning process of integration, suggesting that some may be new to the topic and are navigating through foundational concepts.
Why is the end area of shell [tex]2\pi rdr[/tex]?
Thanks in advance.
- #2
marlon
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PSOA said:
Why is the end area of shell [tex]2\pi rdr[/tex]?
Thanks in advance.
It's the area expressed in differential form. To acquire the correct formula, you need to calculate the integral with respect to r.
Intuitively, the differential form means this : to describe an infinitesimal small area, take the circumference 2 times pi times r and make it a bit thicker, expressed by the dr. Integrating over r means that you sum up the area of all this different, very thin, circumferences to get the total circular area.
marlon
Last edited:
- #3
PSOA
Oh, I got that! Thank you marlon! I am giving my first steps over integration. And congratulations for the award!
- #4
marlon
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What award ?PSOA said:
I just lost my guru badge to somebody else, lol.
marlon