Finding the inertia with a thin rectangular sheet

[kgianqu2]

A) A thin, rectangular sheet of metal has mass M and sides of length a and b. Find the moment of inertia of this sheet about an axis that lies in the plane of the plate, passes through the center of the plate, and is parallel to the side with length b.
Express your answer in terms of given quantities.

attempt at answer: M(a^2+b^2)/12 (mastering physics said the correct answer does not depend on the variable b)

B) Find the moment of inertia of the plate for an axis that lies in the plane of the plate, passes through the center of the plate, and is perpendicular to the axis in part A.
Express your answer in terms of given quantities.

I did not attempt an answer on this part because of the confusion in part A.

Please help, I am very confused about how to input this into mastering physics.

 

[SammyS]

A) A thin, rectangular sheet of metal has mass M and sides of length a and b. Find the moment of inertia of this sheet about an axis that lies in the plane of the plate, passes through the center of the plate, and is parallel to the side with length b.
Express your answer in terms of given quantities.

attempt at answer: M(a^2+b^2)/12 (mastering physics said the correct answer does not depend on the variable b)

That's the moment of inertia about the axis through the center of mass and perpendicular to the sheet.

B) Find the moment of inertia of the plate for an axis that lies in the plane of the plate, passes through the center of the plate, and is perpendicular to the axis in part A.
Express your answer in terms of given quantities.

I did not attempt an answer on this part because of the confusion in part A.

Please help, I am very confused about how to input this into mastering physics.

For part A), think of the sheet as being broken up into thin strips of length a and width Δx .

By the way, you really didn't show your work. You just gave an answer without giving the reasoning behind it.

 

[kgianqu2]

You honestly didn't help at all. I figured it out on my own, thanks a lot. The worst help ever. The answer that I had was basically right, I just had to take out the variable b for the first part, and a for the second part. But thanks for asking where I got the equation from.

 

[SammyS]

You honestly didn't help at all. I figured it out on my own, thanks a lot. The worst help ever. The answer that I had was basically right, I just had to take out the variable b for the first part, and a for the second part. But thanks for asking where I got the equation from.

I glad to have helped.

 

[Nickie]

I would like to clarify the concept of inertia and how it relates to the given problem. Inertia is a property of matter that describes its resistance to change in motion. In the context of rotational motion, inertia is measured by the moment of inertia, which is the rotational equivalent of mass.

In part A of the problem, the moment of inertia is being calculated for an axis that lies in the plane of the rectangular sheet and is parallel to the side with length b. This means that the axis is passing through the center of mass of the sheet, which is also the center of the sheet. The moment of inertia for this axis can be calculated using the formula I = M(a^2 + b^2)/12, where M is the mass of the sheet and a and b are the lengths of its sides. This formula is derived from the parallel axis theorem, which states that the moment of inertia of a body about an axis parallel to its center of mass is equal to the moment of inertia about a parallel axis passing through the center of mass plus the product of the mass and the square of the distance between the two axes.

In part B, the axis of rotation is perpendicular to the axis in part A. This means that the axis is passing through the edge of the sheet instead of the center. In this case, the moment of inertia can be calculated using the formula I = Ma^2/12, where M is the mass of the sheet and a is the length of the side perpendicular to the axis of rotation. This formula is derived from the perpendicular axis theorem, which states that the moment of inertia of a planar body about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two perpendicular axes in the plane of the body.

To input these answers into mastering physics, you can use the given values of M, a, and b to calculate the moment of inertia using the appropriate formula. Be sure to pay attention to the units and make sure they are consistent throughout the calculation. I hope this helps clarify the concept and guide you in solving the problem.