Parallel axis theorem and moment of inertia

[Edwardo_Elric]

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

 

[learningphysics]

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)

 

[m2003]

The moment of inertia for a thin rectangular sheet can be found using the parallel axis theorem, which states that the moment of inertia of a body about any axis is equal to the moment of inertia about a parallel axis through the center of mass plus the product of the mass and the square of the distance between the two axes. In this case, the axis passing through one corner of the sheet is parallel to the axis passing through the center of mass, so the moment of inertia can be calculated using the formula above.

Using the given dimensions and mass, we can find the moment of inertia about the center of mass using the formula for a rectangular plate. Then, we can use the parallel axis theorem to find the moment of inertia about the axis passing through the corner.

Substituting the values into the equations, we get a moment of inertia of approximately 0.05021 kg * m^2. This value represents the resistance of the thin rectangular sheet to changes in its rotational motion about the given axis.