Parallel axis theorem and moment of inertia

AI Thread Summary
To find the moment of inertia of a thin rectangular steel sheet (0.30m x 0.40m, 0.470kg) about an axis through one corner, the parallel axis theorem is applied. The formula used is Ip = Icm + Md^2, where Icm is calculated as 1/12 M(a^2 + b^2). The correct calculation involves ensuring that the mass M is included in the Icm formula. The final moment of inertia is computed as approximately 0.05021 kg*m^2. Accurate application of the formulas is crucial for obtaining the correct result.
Edwardo_Elric
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Homework Statement


A thin rectangular sheet of steel is 0.30m by 0.40m and has mass 0.470kg. Find the moment of inertia about an axis that is perpendicular to the plane of the sheet and that passes through one corner of the sheet.


Homework Equations


Parallel axis theorem:
Ip = Icm + Md^2
Rectangular plate(but not thin):
Icm = 1/12 M(a^2 + b^2) << where a and b are the sides of the rectangle


The Attempt at a Solution



Ip = 1/12((0.30)^2 + (0.40m)^2) + (0.470kg)((0.15m)^2 + (0.20m)^2)
Ip = (0.0208333 + 0.029375)kg * m^2
Ip = 0.05021 kg * m^2
 
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Edwardo_Elric said:

Homework Statement


A thin rectangular sheet of steel is 0.30m by 0.40m and has mass 0.470kg. Find the moment of inertia about an axis that is perpendicular to the plane of the sheet and that passes through one corner of the sheet.


Homework Equations


Parallel axis theorem:
Ip = Icm + Md^2
Rectangular plate(but not thin):
Icm = 1/12 M(a^2 + b^2) << where a and b are the sides of the rectangle


The Attempt at a Solution



Ip = 1/12((0.30)^2 + (0.40m)^2) + (0.470kg)((0.15m)^2 + (0.20m)^2)

you didn't multiply by M... 1/12M (a^2 + b^2)
 
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