Parallel axis theorem and moment of inertia

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SUMMARY

The discussion focuses on calculating the moment of inertia for a thin rectangular sheet of steel measuring 0.30m by 0.40m with a mass of 0.470kg, using the Parallel Axis Theorem. The formula applied is Ip = Icm + Md^2, where Icm for the rectangular plate is calculated as Icm = 1/12 M(a^2 + b^2). The final moment of inertia about an axis perpendicular to the sheet and passing through one corner is determined to be 0.05021 kg * m^2 after correcting for the mass in the calculation.

PREREQUISITES
  • Understanding of the Parallel Axis Theorem
  • Knowledge of moment of inertia calculations
  • Familiarity with rectangular geometry
  • Basic physics principles related to mass and inertia
NEXT STEPS
  • Study the derivation of the Parallel Axis Theorem in detail
  • Learn about moment of inertia for various geometric shapes
  • Explore applications of moment of inertia in engineering and physics
  • Investigate the effects of mass distribution on moment of inertia
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Students in physics or engineering courses, educators teaching mechanics, and professionals involved in structural analysis or material science will benefit from this discussion.

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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