**Practice Exam Rotation II**- A solid sphere with radius \( R \) and a cylindrical hoop with radius \( \frac{1}{3} R \) race down an incline of height \( H \). Determine the final speed of each object as it reaches the bottom of the incline (assume the masses are the same).**Diagrams and Equations:**1. **Cylinder at axis, disc center:** - Diagram shows a cylinder rolling down an incline. - Moment of Inertia: \( \frac{1}{2} MR^2 \)2. **Cylindrical hoop, shear center:** - Diagram shows a hoop rolling down an incline. - Moment of Inertia: \( MR^2 \)3. **Solid sphere, about diameter:** - Diagram shows a sphere rolling down an incline. - Moment of Inertia: \( \frac{2}{5} MR^2 \)4. **Inclined disk or cylinder:** - Diagram shows an inclined disk or cylinder. - Moment of Inertia: \( \frac{1}{2} MR^2 \)The diagrams provide visual representations of each object on an incline with their respective moments of inertia equations, which are key for determining their final speeds at the bottom of the incline.

Given data, Assuming the height of the inclined plane is 'H'. Mass is m v is the velocity.

Kota A solid sphere radius R and a cylindrical hoop radius 1/3 R race down an incline of height H. Determine the final speed of each object as it reaches the bottom of the incline (assume the masses are the same).

Kota A solid sphere radius R and a cylindrical hoop radius 1/3 R race down an incline of height H. Determine the final speed of each object as it reaches the bottom of the incline (assume the masses are the same).

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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Concept explainers

Centripetal Force

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal force.

Question

**Practice Exam Rotation II**

- A solid sphere with radius \( R \) and a cylindrical hoop with radius \( \frac{1}{3} R \) race down an incline of height \( H \). Determine the final speed of each object as it reaches the bottom of the incline (assume the masses are the same).

**Diagrams and Equations:**

1. **Cylinder at axis, disc center:**
- Diagram shows a cylinder rolling down an incline.
- Moment of Inertia: \( \frac{1}{2} MR^2 \)

2. **Cylindrical hoop, shear center:**
- Diagram shows a hoop rolling down an incline.
- Moment of Inertia: \( MR^2 \)

3. **Solid sphere, about diameter:**
- Diagram shows a sphere rolling down an incline.
- Moment of Inertia: \( \frac{2}{5} MR^2 \)

4. **Inclined disk or cylinder:**
- Diagram shows an inclined disk or cylinder.
- Moment of Inertia: \( \frac{1}{2} MR^2 \)

The diagrams provide visual representations of each object on an incline with their respective moments of inertia equations, which are key for determining their final speeds at the bottom of the incline.

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