### 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

See similar textbooks

Related questions

Q: Find the equivalent moment of inertia of the rocker arm assembly with respect to the location of kt…

Q: Determine the moment of inertia and the radius of gyration of the shaded area with respect to the…

Q: 3. If the large ring, small ring, and each spoke weigh 90 lb, 20 lb, and 15 lb respectively. Find…

Q: The welded assembly shown is made from a steel rod which weighs 0.637 lb per foot of length.…

A: Given :steel rod which weighs = 0.637 lb per footAssume a=5.8 inFind : The moment of inertia of the…

Q: For the circular thin plate with a square hole as shown in the image below, if the radius R = 0.29 m…

Q: Determine the moments of inertia of the Z-section about its centroid

Q: the machine element was made from steel by combining a cylindrical base with a cone on top, then…

A: The machine element was made from steel by combining a cylindrical base with a cone on top, and then…

Q: Determine the location y of the center of mass G of the assembly and then calculate the moment of…

A: Data given- Mass of block m1 = 3 kg Mass of semicylinder m2 = 5 kg

Q: A solid cylinder with a radius of 3.9 cm has the same mass as a solid sphere of radius R Part A If…

Q: The slender rods have a mass of 8 kg/m. Suppose that a = 150 mm and b = 250 mm. %3D Determine the…

A: Calculating the mass of the horizontal and vertical rod,

Q: Find the moment of inertia for the cross-sectional shape about the x and y axes, given the function:…

Q: For the area shown, the moment of inertia about axis 1 is 125 in^4 and the total area is 23 in^2. If…

A: Calculate the moment of inertia about its centroidal axis 3.

Q: . The radius of gyration of the 10kg body about an axis passing through point G (center of mass) and…

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.

Question

100%

### 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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Use the given values in problem to answer the following: Find the moment of inertia and radius of gyration of the section of this bar about an axis parallel to x-axis going through the center of gravity of the bar. The bar is symmetrical about the axis parallel to y-axis and going through the center of gravity of the bar and about the axis parallel to z-axis and going through the center of gravity of the bar. The dimensions of the section are: l=51 mm, h=29 mm The triangle: hT=15 mm, lT=18 mm and the 2 circles: diameter=7.4 mm, hC=8 mm, dC=7 mm. A is the origin of the referential axis. Provide an organized table and explain all your steps to find the moment of inertia and radius of gyration about an axis parallel to x-axis and going through the center of gravity of the bar. Does the radius of gyration make sense? In the box below enter the y position of the center of gravity of the bar in mm with one decimal.
Match the most appropriate form of the equation for the moment of inertia to the image shown. All objects are rotating about point O. Note: ris distance, m is a mass, k is a radius of gyration and d is a distance from the mass moment of inertia IG about the center of mass A. D. O M X Mass element Z Rotation axis X A.1=1+md² G B. = SM √² r²dm C.I=mk²_ D.1= Σm,r?
Find the equivalent moment of inertia of the rocker arm assembly with respect to the location of kt. mass1=10kg Jo=20kg-m2 mass2=15kg, a is half of b. The rocker is 30 centimeters long. (kg-m2)
A square panel with a mass of 12 kg is suspended from point C by two ropes at points A and B. If the rope at B is suddenly cut, calculate the tension I in rope A immediately after the cut. The moment of inertia with respect to the center of mass is I = {mb². C 45° 45 A B b b (Ctrl)
Find the moments of inertia of the shaded shape about the given centroidal x-axis (Ix) and centroidal y-axis (I). The equations for a single rectangle's moment of inertia about its own centroidal axis is given below. 4 h + y с A = bh Rectangular area X I₂ = 1/2bh³ bh³ Iy = 1 in 2 in 2 in y 1 in 2 in y' x' 2.375 in X
please show all steps
Equation of Motion The triangle is made of 3 rods of a length 1-2.1ft and density is p = 4 lb/ft. ^ 1) Establish what you think is the best Coordinate system for this problem and explain why. 2) Find the location of the center of gravity (x bar and y bar). 3) Find the weight of the triangle. 4) Find the Mass Moment of Inertia at O of the triangle. 5) Draw the FBD and kinetic diagram of the triangle. 6) Find the accelerations of the triangle (angular and linear). 7) Find the Pin Reaction at O: . On and Ot • or Ox and Oy . • Magnitude O, and direction. In the box below, enter the angular acceleration & in rad/s with one decimal. Include the sign + if CCW or - sign if CW.
Compute the moment of inertia about x-axis. r = 4m X 10 m 4 m O 88.37 m^4 O 445.25 m^4 195.04 m^4 508.96 m^4
A |7 Not Quarter-circle L = 0.11 0.11 Semi-circle I= 0.11 -2 6 2 0 Determine the moment of inertia and radius of gyration about the x- axis for the quarter-circle and the semi-circle. Grid units are [mm]. NY 2 * k= X * k = 0.264 X
wheel with a mass of 20 kg and a radius of inertia of 300mm, moves under the influence of a torque of 100Nm. Find the angular acceleration of the wheel, the linear acceleration of its center O, the wheel pressure n the ground N, and the mass moment of inertia J. Give the result to 2 decimal places.
5. Calculate the moments of inertia I1, I2, and I3 for a homogeneous cone of mass M whose height is h and whose base has a radius R. Choose the origin at the apex of the cone, and calculate the elements of the inertia tensor. Then make a transformation such that the center of mass of the cone becomes the origin, and find the principal moments of inertia.
Answer is wrong. Please proviode correct answer