Answered: A composite pendulum is made of a…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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$**Educational Content: Understanding Moment of Inertia in Composite Pendulums** A composite pendulum is composed of a uniform slender rod and a uniform disk. For this problem, consider: - **Rod** - Length: 1.5 m - Mass: 10.5 kg - **Disk** - Radius: 0.24 m - Mass: 7.1 kg **Objective:** To determine the mass moment of inertia ($ \text{kg} \cdot \text{m}^2 $) about the centroidal x-axis passing through its center of gravity, as seen from the profile view. **Important Note:** The numbers used in this exercise may be randomized each time. Ensure your answer includes two decimal places. **Diagram Explanation:** - The left side illustrates the configuration with both rod and disk. - The rod is vertical with length $ l $, and a disk is attached at the bottom. - $ G $ marks the center of gravity for each component. - Variables $ \overline{y} $ and $ x $ represent specific measurements within the system. **How to Solve:** 1. Calculate the moment of inertia for both the rod and the disk separately about the x-axis. 2. Use parallel axis theorem if necessary. 3. Sum the moments of inertia to get the total moment of inertia for the composite pendulum. Your calculations should reflect these steps to provide the correct answer. **Input Your Answer:** [Answer Box] --- This exercise reinforces concepts of inertia calculation in mechanical systems, important for physics and engineering applications.$

Transcribed Image Text:**Educational Content: Understanding Moment of Inertia in Composite Pendulums** A composite pendulum is composed of a uniform slender rod and a uniform disk. For this problem, consider: - **Rod** - Length: 1.5 m - Mass: 10.5 kg - **Disk** - Radius: 0.24 m - Mass: 7.1 kg **Objective:** To determine the mass moment of inertia ($ \text{kg} \cdot \text{m}^2 $) about the centroidal x-axis passing through its center of gravity, as seen from the profile view. **Important Note:** The numbers used in this exercise may be randomized each time. Ensure your answer includes two decimal places. **Diagram Explanation:** - The left side illustrates the configuration with both rod and disk. - The rod is vertical with length $ l $, and a disk is attached at the bottom. - $ G $ marks the center of gravity for each component. - Variables $ \overline{y} $ and $ x $ represent specific measurements within the system. **How to Solve:** 1. Calculate the moment of inertia for both the rod and the disk separately about the x-axis. 2. Use parallel axis theorem if necessary. 3. Sum the moments of inertia to get the total moment of inertia for the composite pendulum. Your calculations should reflect these steps to provide the correct answer. **Input Your Answer:** [Answer Box] --- This exercise reinforces concepts of inertia calculation in mechanical systems, important for physics and engineering applications.

$**Problem Statement:** A composite pendulum is made of a uniform slender rod and a uniform disk. If the rod has a length of 0.8 m and a mass of 13.2 kg, and the disk has a radius of 0.23 m and a mass of 8.5 kg, determine the location $ \bar{y} $ of the centroidal x-axis. Please pay attention: **the numbers may change** since they are randomized. Your answer must include 3 places after the decimal point, and proper units. **Diagram Explanation:** The diagram shows a profile view of the composite pendulum made up of two components: 1. A slender rod of length $ l $. 2. A disk of radius $ R $. - The rod is shown as a vertical line with its length labeled $ l = 0.8 \, \text{m} $. - The center of mass of the rod is marked as $ G $ along the rod. - The disk is attached at the end of the rod, with its center of mass also marked as $ G $. - The horizontal axis $ x $ runs along the top of the assembly, and the vertical distance $ \bar{y} $ from this axis to the centroid of the pendulum is marked with a red arrow. **Answer Section:** The answer should be entered in the provided text box with three decimal places and appropriate units. **Your Answer:** \[ \text{Answer:} \quad \_\_\_\_\_\_ \quad \text{units} \]$

Transcribed Image Text:**Problem Statement:** A composite pendulum is made of a uniform slender rod and a uniform disk. If the rod has a length of 0.8 m and a mass of 13.2 kg, and the disk has a radius of 0.23 m and a mass of 8.5 kg, determine the location $ \bar{y} $ of the centroidal x-axis. Please pay attention: **the numbers may change** since they are randomized. Your answer must include 3 places after the decimal point, and proper units. **Diagram Explanation:** The diagram shows a profile view of the composite pendulum made up of two components: 1. A slender rod of length $ l $. 2. A disk of radius $ R $. - The rod is shown as a vertical line with its length labeled $ l = 0.8 \, \text{m} $. - The center of mass of the rod is marked as $ G $ along the rod. - The disk is attached at the end of the rod, with its center of mass also marked as $ G $. - The horizontal axis $ x $ runs along the top of the assembly, and the vertical distance $ \bar{y} $ from this axis to the centroid of the pendulum is marked with a red arrow. **Answer Section:** The answer should be entered in the provided text box with three decimal places and appropriate units. **Your Answer:** \[ \text{Answer:} \quad \_\_\_\_\_\_ \quad \text{units} \]

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