**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.

AIM: To determine the position of center of mass and moment of inertia for a given system of masses…

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

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)...

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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.

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