Calculate (*) the center of mass for the following system composed of objects positioned along a massless rod and (**) the moment of inertia for the system if an axis of rotation is located at the 1 m mark. 12 kg 0m 1 m 2 m

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
icon
Related questions
Question
**Title: Calculating Center of Mass and Moment of Inertia**

**Objective:**
- (*) Calculate the center of mass for the system composed of objects positioned along a massless rod.
- (**) Calculate the moment of inertia for the system if an axis of rotation is located at the 1 m mark.

**Diagram:**

- The system consists of three masses arranged on a straight, massless rod:
  - A 3 kg mass is located at 0.5 meters.
  - A 12 kg mass is located at 1.0 meters.
  - A 9 kg mass is located at 1.5 meters.

**Center-of-Mass Options:**

A. 1.196 m  
B. 1.038 m  
C. 0.8676 m  
D. 0.8173 m  
E. 1.240 m  
F. 1.028 m  

**Moment of Inertia Options:**

A. 11.04 kg·m²  
B. 11.50 kg·m²  
C. 9.270 kg·m²  
D. 9.040 kg·m²  
E. 9.226 kg·m²  
F. 8.638 kg·m²  

**Explanation:**

- **Center of Mass Calculation:**
  The center of mass is obtained by taking the weighted average of the positions of the masses.

- **Moment of Inertia Calculation:**
  The moment of inertia about an axis is calculated using the formula \( I = \sum m_i \times r_i^2 \), where \( m_i \) is the mass and \( r_i \) is the distance from the axis of rotation. Here, calculate the moment of inertia with respect to the axis at the 1 m mark.

Ensure to verify calculations based on the mass positions and given options.
Transcribed Image Text:**Title: Calculating Center of Mass and Moment of Inertia** **Objective:** - (*) Calculate the center of mass for the system composed of objects positioned along a massless rod. - (**) Calculate the moment of inertia for the system if an axis of rotation is located at the 1 m mark. **Diagram:** - The system consists of three masses arranged on a straight, massless rod: - A 3 kg mass is located at 0.5 meters. - A 12 kg mass is located at 1.0 meters. - A 9 kg mass is located at 1.5 meters. **Center-of-Mass Options:** A. 1.196 m B. 1.038 m C. 0.8676 m D. 0.8173 m E. 1.240 m F. 1.028 m **Moment of Inertia Options:** A. 11.04 kg·m² B. 11.50 kg·m² C. 9.270 kg·m² D. 9.040 kg·m² E. 9.226 kg·m² F. 8.638 kg·m² **Explanation:** - **Center of Mass Calculation:** The center of mass is obtained by taking the weighted average of the positions of the masses. - **Moment of Inertia Calculation:** The moment of inertia about an axis is calculated using the formula \( I = \sum m_i \times r_i^2 \), where \( m_i \) is the mass and \( r_i \) is the distance from the axis of rotation. Here, calculate the moment of inertia with respect to the axis at the 1 m mark. Ensure to verify calculations based on the mass positions and given options.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 6 images

Blurred answer
Knowledge Booster
Rotational Kinetic energy
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON