### Determine the Moment of InertiaThe uniform rod of length \(4b\) and mass \(m\) is bent into the shape shown. The diameter of the rod is small compared with its length. Determine the moments of inertia of the rod about the three coordinate axes. Use the values \(m = 7.9 \text{ kg}\) and \(b = 485 \text{ mm}\).#### Diagram Explanation:The diagram illustrates a rod bent into a 3D shape, which appears to be forming a series of right angles. The rod is divided into sections of \(b\) length each as follows:1. **Section OA** - Vertical segment with length \(b\)2. **Section AB** - Horizontal segment with length \(b\)3. **Section BC** - Vertical segment with length \(b\)4. **Section CD** - Horizontal segment with length \(b\)The shape is designed to lie in three planes, and the provided \(x\), \(y\), and \(z\) coordinate system highlights the axis of rotation.#### Calculation:To determine the moments of inertia \(I_{xx}\), \(I_{yy}\), and \(I_{zz}\) about the respective axes, consider the following calculations and representations:1. **Moment of Inertia about the x-axis (Ixx):** - This involves calculating the contributions of each section's distance from the x-axis.2. **Moment of Inertia about the y-axis (Iyy):** - Similar calculation for each section's distance from the y-axis.3. **Moment of Inertia about the z-axis (Izz):** - Calculation involves the length and mass distribution relative to the z-axis.#### Given:- Mass (\(m\)) = 7.9 kg- Length (\(b\)) = 485 mm = 0.485 m#### Answers:Kindly input your calculated values for moments of inertia in the respective fields below:- \( I_{xx} \) = __________ kg·m²- \( I_{yy} \) = __________ kg·m²- \( I_{zz} \) = __________ kg·m²Please ensure that your unit conversions are accurate and that you utilize the parallel axis theorem as needed for calculating the moments of inertia about different axes.

Draw the given diagram with 3 sections. Calculate the distances r1 and r2 as shown in above…

The uniform rod of length 4b and mass m is bent into the shape shown. The diameter of the rod is small compared with its length. Determine the moments of inertia of the rod about the three coordinate axes. Use the values m = 7.9 kg and b=485 mm. Answers: lxx= lyy= Izz = i i i kg-m² kg-m² kg-m²

The uniform rod of length 4b and mass m is bent into the shape shown. The diameter of the rod is small compared with its length. Determine the moments of inertia of the rod about the three coordinate axes. Use the values m = 7.9 kg and b=485 mm. Answers: lxx= lyy= Izz = i i i kg-m² kg-m² kg-m²

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.87RP

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Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.

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### Determine the Moment of Inertia

The uniform rod of length \(4b\) and mass \(m\) is bent into the shape shown. The diameter of the rod is small compared with its length. Determine the moments of inertia of the rod about the three coordinate axes. Use the values \(m = 7.9 \text{ kg}\) and \(b = 485 \text{ mm}\).

#### Diagram Explanation:
The diagram illustrates a rod bent into a 3D shape, which appears to be forming a series of right angles. The rod is divided into sections of \(b\) length each as follows:

1. **Section OA** - Vertical segment with length \(b\)
2. **Section AB** - Horizontal segment with length \(b\)
3. **Section BC** - Vertical segment with length \(b\)
4. **Section CD** - Horizontal segment with length \(b\)

The shape is designed to lie in three planes, and the provided \(x\), \(y\), and \(z\) coordinate system highlights the axis of rotation.

#### Calculation:
To determine the moments of inertia \(I_{xx}\), \(I_{yy}\), and \(I_{zz}\) about the respective axes, consider the following calculations and representations:

1. **Moment of Inertia about the x-axis (I<sub>xx</sub>):**
- This involves calculating the contributions of each section's distance from the x-axis.

2. **Moment of Inertia about the y-axis (I<sub>yy</sub>):**
- Similar calculation for each section's distance from the y-axis.

3. **Moment of Inertia about the z-axis (I<sub>zz</sub>):**
- Calculation involves the length and mass distribution relative to the z-axis.

#### Given:
- Mass (\(m\)) = 7.9 kg
- Length (\(b\)) = 485 mm = 0.485 m

#### Answers:
Kindly input your calculated values for moments of inertia in the respective fields below:

- \( I_{xx} \) = __________ kg·m²
- \( I_{yy} \) = __________ kg·m²
- \( I_{zz} \) = __________ kg·m²

Please ensure that your unit conversions are accurate and that you utilize the parallel axis theorem as needed for calculating the moments of inertia about different axes.

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