# Moment of Inertia of a Rectangular Picture Frame

• kepherax
In summary, the problem involves determining the rotational inertia of a picture frame consisting of 4 thin pieces of wood with the same mass per unit length. The dimensions of each piece are given and the goal is to find the inertia about a dashed axis. The solution involves using the formula I = mr^2 for a rod at the edge, and the total inertia can be found by adding up the individual inertias of each piece. To find the inertia of a small element of one of the spars, the distance from the axis is calculated to be xsin(angle) and then integrated. Alternatively, the problem can be simplified by considering the spar as having the same mass but length Lsin(angle) and perpendicular to the axis.
kepherax
Homework Statement
A picture frame consists of 4 thin pieces of wood glued together. Each wooden piece has the same mass per unit length lambda. The dimensions of each piece is given below. Determine the rotational inertia of the frame about the dashed axis.
Relevant Equations
I = mr^2, for rod at edge I = 1/3 mr^2
I total = I1+I2+I3....+In
https://www.physicsforums.com/attachments/250905

I know the answer, but am not certain how they got Lsin(angle) for R?

Last edited:
kepherax said:
Homework Statement: A picture frame consists of 4 thin pieces of wood glued together. Each wooden piece has the same mass per unit length lambda. The dimensions of each piece is given below. Determine the rotational inertia of the frame about the dashed axis.
Homework Equations: I = mr^2, for rod at edge I = 1/3 mr^2
I total = I1+I2+I3...+In

https://www.physicsforums.com/attachments/250905

I know the answer, but am not certain how they got Lsin(angle) for R?
The link does not work for me. Please post an attempt, per forum rules.

I don't know why it won't let me edit this, but here is the problem and my attempt.

kepherax said:
how they got Lsin(angle) for R?
Consider a small element dx of one of the spars length L, distance x from the end at the axis.
Its distance from the axis is ##x\sin(\theta)##, so its MoI about the axis is ##\lambda dx (x\sin(\theta))^2##. Then integrate, or observe that this is the same as if the spar were the same mass but length ##L\sin(\theta)## and normal to the axis.

## 1. What is the moment of inertia of a rectangular picture frame?

The moment of inertia of a rectangular picture frame is a measure of its resistance to rotational motion. It is a property of an object that depends on its mass distribution and the axis of rotation.

## 2. How is the moment of inertia of a rectangular picture frame calculated?

The moment of inertia of a rectangular picture frame can be calculated using the formula I = (1/12) * m * (h^2 + w^2), where I is the moment of inertia, m is the mass of the frame, h is the height, and w is the width.

## 3. What factors affect the moment of inertia of a rectangular picture frame?

The moment of inertia of a rectangular picture frame is affected by its mass, shape, and distribution of mass. A frame with a larger mass or a wider width will have a larger moment of inertia.

## 4. How does the moment of inertia of a rectangular picture frame affect its stability?

The moment of inertia of a rectangular picture frame is directly proportional to its stability. A frame with a larger moment of inertia will be more stable and less likely to tip over.

## 5. Can the moment of inertia of a rectangular picture frame be changed?

Yes, the moment of inertia of a rectangular picture frame can be changed by altering its mass distribution. For example, adding weight to one side of the frame will increase its moment of inertia in that direction.

• Introductory Physics Homework Help
Replies
11
Views
436
• Introductory Physics Homework Help
Replies
28
Views
681
• Introductory Physics Homework Help
Replies
25
Views
710
• Introductory Physics Homework Help
Replies
52
Views
3K
• Introductory Physics Homework Help
Replies
40
Views
3K
• Introductory Physics Homework Help
Replies
2
Views
825
• Introductory Physics Homework Help
Replies
13
Views
2K
• Introductory Physics Homework Help
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
14
Views
879
• Introductory Physics Homework Help
Replies
4
Views
1K