Parallel Axis Theorem and sheet of metal

[physstudent1]

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

 

[CompuChip]

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)?

 

[physstudent1]

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

 

[physstudent1]

anyone?

 

[Doc Al]

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.

 

[inky]

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