### Chapter 8 Homework#### Current Attempt in ProgressA string trimmer is a tool for cutting grass and weeds; it utilizes a length of nylon "string" that rotates about an axis perpendicular to one end of the string. The string rotates at an angular speed of 42 rev/s, and its tip has a tangential speed of 67 m/s. What is the length of the rotating string?**Answer Submission:**- **Number**: [Input field for numeric answer]- **Units**: [Dropdown menu for selecting units]**Options:**- [Checkbox] Save for Later**Submission Button:**- **Attempts**: 0 of 5 used- [Submit Answer button]*Note*: Please make sure to save your progress if you wish to return to this question later.**Explanation for the Diagram/Graph:**There are no graphs or diagrams associated with this question.**Navigation:**- **Previous Page Button:** [<]- **Next Page Button:** [>]This problem requires understanding the relationship between angular speed, tangential speed, and the radius of rotation for the string trimmer. To solve for the length of the rotating string, you can use the formula relating tangential speed (v), angular speed (ω), and radius (r):\[ v = r \cdot \omega \]Given:- Angular speed, \( \omega = 42 \) rev/s (note: you may need to convert this to radians/s)- Tangential speed, \( v = 67 \) m/sSolving for \( r \) will give you the length of the rotating string.---For additional help and resources, be sure to review the relevant section in your textbook or consult your instructor.

Answered: Image /qna-images/answer/cd0b58b5-3bbb-464a-aade-27779e8c75fa.jpg

A string trimmer is a tool for cutting grass and weeds; it utilizes a length of nylon "string" that rotates about an axis perpendicular to one end of the string. The string rotates at an angular speed of 42 rev/s, and its tip has a tangential speed of 67 m/s. What is the length of the rotating string?

A string trimmer is a tool for cutting grass and weeds; it utilizes a length of nylon "string" that rotates about an axis perpendicular to one end of the string. The string rotates at an angular speed of 42 rev/s, and its tip has a tangential speed of 67 m/s. What is the length of the rotating string?

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

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

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### Chapter 8 Homework

#### Current Attempt in Progress

A string trimmer is a tool for cutting grass and weeds; it utilizes a length of nylon "string" that rotates about an axis perpendicular to one end of the string. The string rotates at an angular speed of 42 rev/s, and its tip has a tangential speed of 67 m/s. What is the length of the rotating string?

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This problem requires understanding the relationship between angular speed, tangential speed, and the radius of rotation for the string trimmer. To solve for the length of the rotating string, you can use the formula relating tangential speed (v), angular speed (ω), and radius (r):
\[ v = r \cdot \omega \]
Given:
- Angular speed, \( \omega = 42 \) rev/s (note: you may need to convert this to radians/s)
- Tangential speed, \( v = 67 \) m/s

Solving for \( r \) will give you the length of the rotating string.

---
For additional help and resources, be sure to review the relevant section in your textbook or consult your instructor.

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