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Consider the toy represented in the image. This toy is made by attaching a ball of mass m to a wooden stick by means of two identical strings, each of which makes an angle with the stick. When you rotate the stick between the palms of your hands, the ball travels in a circle of radius R at constant speed v. In the diagram gravity points down, and the circular path of the ball is flat and in a plane that is parallel with the ground. e string 1 Ꮎ R 0 string 2 Ꮎ

Consider the toy represented in the image. This toy is made by attaching a ball of mass m to a wooden stick by means of two identical strings, each of which makes an angle with the stick. When you rotate the stick between the palms of your hands, the ball travels in a circle of radius R at constant speed v. In the diagram gravity points down, and the circular path of the ball is flat and in a plane that is parallel with the ground. e string 1 Ꮎ R 0 string 2 Ꮎ

College Physics
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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### Educational Content on Rotational Motion Toy **Title: Understanding Rotational Motion through a Simple Toy** **Description:** Consider the toy represented in the image. This toy is made by attaching a ball of mass \( m \) to a wooden stick by means of two identical strings, each of which makes an angle \( \theta \) with the stick. When you rotate the stick between the palms of your hands, the ball travels in a circle of radius \( R \) at constant speed \( v \). In the diagram, gravity points down, and the circular path of the ball is flat and in a plane that is parallel with the ground. **Detailed Diagram Explanation:** The diagram shows a vertical wooden stick with two strings attached to it. The strings hold a ball that revolves around the stick when the stick is rotated. Here’s a detailed explanation of the components: 1. **Wooden Stick:** - Represented in yellow color. - Held vertically. 2. **Strings:** - There are two identical strings labeled "string 1" and "string 2". - Both strings are attached to the stick at different heights. - Each string creates an angle \( \theta \) with the wooden stick. 3. **Ball:** - Shown in blue color, attached to the two strings. - It has a mass \( m \). 4. **Path of the Ball:** - The ball moves in a circular path when the stick is rotated. - The radius \( R \) of the circular path is shown. - The circular path is indicated by a dashed line with arrows showing the direction of motion. 5. **Angles and Measurements:** - The angle \( \theta \) is the same for both strings relative to the stick. - \( R \) is the radius of the circular path, measured from the center of the stick to the path of the ball. This setup can help in understanding concepts related to circular motion, centripetal force, and rotational dynamics. By analyzing this system, one can explore the forces involved in maintaining the ball’s circular path and derive relationships between the various physical quantities like tension in the strings, radius of the path \( R \), and the speed \( v \) of the rotating ball.
Transcribed Image Text:### Educational Content on Rotational Motion Toy **Title: Understanding Rotational Motion through a Simple Toy** **Description:** Consider the toy represented in the image. This toy is made by attaching a ball of mass \( m \) to a wooden stick by means of two identical strings, each of which makes an angle \( \theta \) with the stick. When you rotate the stick between the palms of your hands, the ball travels in a circle of radius \( R \) at constant speed \( v \). In the diagram, gravity points down, and the circular path of the ball is flat and in a plane that is parallel with the ground. **Detailed Diagram Explanation:** The diagram shows a vertical wooden stick with two strings attached to it. The strings hold a ball that revolves around the stick when the stick is rotated. Here’s a detailed explanation of the components: 1. **Wooden Stick:** - Represented in yellow color. - Held vertically. 2. **Strings:** - There are two identical strings labeled "string 1" and "string 2". - Both strings are attached to the stick at different heights. - Each string creates an angle \( \theta \) with the wooden stick. 3. **Ball:** - Shown in blue color, attached to the two strings. - It has a mass \( m \). 4. **Path of the Ball:** - The ball moves in a circular path when the stick is rotated. - The radius \( R \) of the circular path is shown. - The circular path is indicated by a dashed line with arrows showing the direction of motion. 5. **Angles and Measurements:** - The angle \( \theta \) is the same for both strings relative to the stick. - \( R \) is the radius of the circular path, measured from the center of the stick to the path of the ball. This setup can help in understanding concepts related to circular motion, centripetal force, and rotational dynamics. By analyzing this system, one can explore the forces involved in maintaining the ball’s circular path and derive relationships between the various physical quantities like tension in the strings, radius of the path \( R \), and the speed \( v \) of the rotating ball.
**Drawing and Analyzing Free-Body Diagrams in Physics** **Objective:** Draw a free-body diagram where the system is the ball at the location shown in the diagram. Your diagram should include all the relevant axes and all the forces acting on the ball in the correct directions and with correct angles, where applicable. **Instructions:** - **Axes Identification**: It's crucial to correctly identify and label the axes in your diagram. Remember to think about the \( \hat{p} \), \( \hat{n} \), and \( \hat{y} \) axes in this problem. - **Force Representation**: Include all forces acting on the ball in correct magnitude and direction. - **Angles**: Ensure that the angles formed by the forces and axes are accurately depicted. **Hint**: Think of what are the \( \hat{p} \), \( \hat{n} \), and \( \hat{y} \) axes in relation to your problem. These notations might refer to different coordinates or specific vectors pertinent to your scenario, such as perpendicular, normal, or any other direction that is significant. --- Use this information to develop a detailed understanding of analyzing forces in a system and accurately represent physical phenomena through free-body diagrams.
Transcribed Image Text:**Drawing and Analyzing Free-Body Diagrams in Physics** **Objective:** Draw a free-body diagram where the system is the ball at the location shown in the diagram. Your diagram should include all the relevant axes and all the forces acting on the ball in the correct directions and with correct angles, where applicable. **Instructions:** - **Axes Identification**: It's crucial to correctly identify and label the axes in your diagram. Remember to think about the \( \hat{p} \), \( \hat{n} \), and \( \hat{y} \) axes in this problem. - **Force Representation**: Include all forces acting on the ball in correct magnitude and direction. - **Angles**: Ensure that the angles formed by the forces and axes are accurately depicted. **Hint**: Think of what are the \( \hat{p} \), \( \hat{n} \), and \( \hat{y} \) axes in relation to your problem. These notations might refer to different coordinates or specific vectors pertinent to your scenario, such as perpendicular, normal, or any other direction that is significant. --- Use this information to develop a detailed understanding of analyzing forces in a system and accurately represent physical phenomena through free-body diagrams.
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