**Moments of Inertia for Various Rigid Objects of Uniform Composition**Four objects—a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell—each have a mass of 4.33 kg and a radius of 0.264 m. **Objective:**(a) Find the moment of inertia for each object as it rotates about the axes shown in the illustrations below.**Illustrations of Objects:**1. **Hoop or Thin Cylindrical Shell** - Axis of rotation is perpendicular to the circular face and passing through the center. - Formula for Moment of Inertia: \(I = MR^2\)2. **Solid Cylinder or Disk** - Axis of rotation is perpendicular to the circular face and passing through the center. - Formula for Moment of Inertia: \(I = \frac{1}{2} MR^2\)3. **Solid Sphere** - Axis of rotation passes through the center of the sphere. - Formula for Moment of Inertia: \(I = \frac{2}{5} MR^2\)4. **Thin Spherical Shell** - Axis of rotation passes through the center of the shell. - Formula for Moment of Inertia: \(I = \frac{2}{3} MR^2\)5. **Long, Thin Rod with Rotation Axis Through Center** - Axis of rotation is perpendicular to the length of the rod and passing through the center. - Formula for Moment of Inertia: \(I = \frac{1}{12} ML^2\)6. **Long, Thin Rod with Rotation Axis Through End** - Axis of rotation is perpendicular to the length of the rod and passing through one end. - Formula for Moment of Inertia: \(I = \frac{1}{3} ML^2\)**Note:** The formulas provided are specific to the rotation axes illustrated for each object.**Table for Calculated Moments of Inertia:**- Hoop: _____ kg·m²- Solid Cylinder: _____ kg·m² - Solid Sphere: _____ kg·m²- Thin Spherical Shell: _____ kg·m²Use these formulas to calculate the moments of inertia based on the given mass and radius for the hoop, solid cylinder, solid sphere, and thin spherical shell.

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Four objects-a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell-each have a mass of 4.33 kg and a radius of 0.264 m. (a) Find the moment of inertia for each object as it rotates about the axes shown in the table below. Moments of Inertia for Various Rigid Objects of Uniform Composition Hoop or thin cylindrical shell 1 = MR Solid sphere 1- M Solid cylinder or disk Thin spherical shell 1-MR MR2 Long, hin rod with rotation axis through center Long, thin rod with rotation axis I- through end ML? hoop kg - m2 solid cylinder kg - m2 kg - m2 solid sphere thin, spherical shell kg - m2

Four objects-a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell-each have a mass of 4.33 kg and a radius of 0.264 m. (a) Find the moment of inertia for each object as it rotates about the axes shown in the table below. Moments of Inertia for Various Rigid Objects of Uniform Composition Hoop or thin cylindrical shell 1 = MR Solid sphere 1- M Solid cylinder or disk Thin spherical shell 1-MR MR2 Long, hin rod with rotation axis through center Long, thin rod with rotation axis I- through end ML? hoop kg - m2 solid cylinder kg - m2 kg - m2 solid sphere thin, spherical shell kg - m2

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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Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

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**Moments of Inertia for Various Rigid Objects of Uniform Composition**

Four objects—a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell—each have a mass of 4.33 kg and a radius of 0.264 m.

**Objective:**
(a) Find the moment of inertia for each object as it rotates about the axes shown in the illustrations below.

**Illustrations of Objects:**

1. **Hoop or Thin Cylindrical Shell**
- Axis of rotation is perpendicular to the circular face and passing through the center.
- Formula for Moment of Inertia: \(I = MR^2\)

2. **Solid Cylinder or Disk**
- Axis of rotation is perpendicular to the circular face and passing through the center.
- Formula for Moment of Inertia: \(I = \frac{1}{2} MR^2\)

3. **Solid Sphere**
- Axis of rotation passes through the center of the sphere.
- Formula for Moment of Inertia: \(I = \frac{2}{5} MR^2\)

4. **Thin Spherical Shell**
- Axis of rotation passes through the center of the shell.
- Formula for Moment of Inertia: \(I = \frac{2}{3} MR^2\)

5. **Long, Thin Rod with Rotation Axis Through Center**
- Axis of rotation is perpendicular to the length of the rod and passing through the center.
- Formula for Moment of Inertia: \(I = \frac{1}{12} ML^2\)

6. **Long, Thin Rod with Rotation Axis Through End**
- Axis of rotation is perpendicular to the length of the rod and passing through one end.
- Formula for Moment of Inertia: \(I = \frac{1}{3} ML^2\)

**Note:** The formulas provided are specific to the rotation axes illustrated for each object.

**Table for Calculated Moments of Inertia:**

- Hoop: _____ kg·m²
- Solid Cylinder: _____ kg·m²
- Solid Sphere: _____ kg·m²
- Thin Spherical Shell: _____ kg·m²

Use these formulas to calculate the moments of inertia based on the given mass and radius for the hoop, solid cylinder, solid sphere, and thin spherical shell.

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