Parallel Axis Theorem and sheet of metal

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Homework Help Overview

The problem involves calculating the moment of inertia of a thin, rectangular sheet of metal using the parallel-axis theorem. The focus is on determining the moment of inertia for an axis perpendicular to the plane of the sheet that passes through one corner.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the identification of the axis of rotation and the necessary components to apply the parallel-axis theorem, including the moment of inertia about the center of mass (Icm) and the distance (d) from the center of mass to the new axis.

Discussion Status

Some participants are exploring the calculation of Icm for the rectangular sheet and questioning the axis of rotation. There is an ongoing dialogue about the correct values to use and how to visualize the problem, with some guidance provided on looking up the moment of inertia for a rectangular sheet.

Contextual Notes

Participants express uncertainty about the axis of rotation and the implications of the problem setup, indicating a need for clarification on these points. There is mention of the problem being from a textbook, which may impose specific constraints or expectations.

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Homework Statement


A thin, rectangular sheet of metal has a mass M and sides of length a and b. Use the parallel-axis theorem to calculate the moment of inertia of the sheet for an axis that is perpendicular to the plane of the sheet that passes through one corner of the sheet

Homework Equations





The Attempt at a Solution



I'm not really sure what axis the problem is saying that the sheet will be rotating around I know the answer is 1/3M(a^2 + b^2) because this is an odd problem in my book, but I'm not sure how to go about it. I know the parallel axis theorem is I = Icm +Md^2
 
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Just try step by step to find all the ingredients to apply the parallel axis theorem.
Like: what is Icm? What is it in this case? Can you look it up, or calculate it?
Then, what is d (draw a picture, and then try to get a formula from that)?
 
i was thinking that the Icm was 1/3Ma^2 the distance I'm not sure about because I am not sure hwat axis it is rotating about
 
anyone?
 
physstudent1 said:
i was thinking that the Icm was 1/3Ma^2
No. Look up the rotational inertia of a rectangular sheet.
the distance I'm not sure about because I am not sure hwat axis it is rotating about
Pick any corner. The distance from the cm will be the same.
 
For rectangular sheet
I[CM]=(1/12)M(a^2+b^2)

I(corner) means parallel to x-axis or y axis.

I=I[x]+Md^2
I=(1/12)Mb^2+M(b/2)^2=(1/3)Mb^2
 

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