### Question 5 A child is sitting on the outer edge of a merry-go-round that is 18 m in diameter. If the merry-go-round makes 4.9 rev/min, what is the velocity of the child in m/s? - A. 4.6 m/s - B. 3.2 m/s - C. 0.7 m/s - D. 9.2 m/s **Instructions:** Click Save and Submit to save and submit. Click Save All Answers to save all answers. --- ### Explanation: To calculate the velocity, we need to use the formula for the linear velocity of an object in circular motion: \[ v = r \cdot \omega \] Where: - \( v \) is the linear velocity. - \( r \) is the radius of the circular path. - \( \omega \) is the angular velocity in radians per second. 1. First, find the radius of the merry-go-round: \[ r = \frac{\text{diameter}}{2} = \frac{18\, \text{m}}{2} = 9\, \text{m} \] 2. Convert the angular velocity from revolutions per minute to radians per second: \[ 4.9\, \text{rev/min} \cdot \frac{2\pi\, \text{radians}}{1\, \text{rev}} \cdot \frac{1\, \text{min}}{60\, \text{s}} = 4.9 \cdot \frac{2\pi}{60} \, \text{rad/s} \] 3. Calculate the angular velocity: \[ \omega = 4.9 \cdot \frac{\pi}{30} \approx 0.514\, \text{rad/s} \] 4. Now calculate the linear velocity: \[ v = r \cdot \omega = 9\, \text{m} \cdot 0.514\, \text{rad/s} \approx 4.63\, \text{m/s} \] Therefore, the correct answer is: - **A. 4.6 m/s** Note: While the detailed explanation provides insight into how the velocity is computed, students are encouraged to practice solving these steps to enhance their understanding of circular motion and angular velocity.
### Question 5 A child is sitting on the outer edge of a merry-go-round that is 18 m in diameter. If the merry-go-round makes 4.9 rev/min, what is the velocity of the child in m/s? - A. 4.6 m/s - B. 3.2 m/s - C. 0.7 m/s - D. 9.2 m/s **Instructions:** Click Save and Submit to save and submit. Click Save All Answers to save all answers. --- ### Explanation: To calculate the velocity, we need to use the formula for the linear velocity of an object in circular motion: \[ v = r \cdot \omega \] Where: - \( v \) is the linear velocity. - \( r \) is the radius of the circular path. - \( \omega \) is the angular velocity in radians per second. 1. First, find the radius of the merry-go-round: \[ r = \frac{\text{diameter}}{2} = \frac{18\, \text{m}}{2} = 9\, \text{m} \] 2. Convert the angular velocity from revolutions per minute to radians per second: \[ 4.9\, \text{rev/min} \cdot \frac{2\pi\, \text{radians}}{1\, \text{rev}} \cdot \frac{1\, \text{min}}{60\, \text{s}} = 4.9 \cdot \frac{2\pi}{60} \, \text{rad/s} \] 3. Calculate the angular velocity: \[ \omega = 4.9 \cdot \frac{\pi}{30} \approx 0.514\, \text{rad/s} \] 4. Now calculate the linear velocity: \[ v = r \cdot \omega = 9\, \text{m} \cdot 0.514\, \text{rad/s} \approx 4.63\, \text{m/s} \] Therefore, the correct answer is: - **A. 4.6 m/s** Note: While the detailed explanation provides insight into how the velocity is computed, students are encouraged to practice solving these steps to enhance their understanding of circular motion and angular velocity.
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)...
Related questions
Question
![### Question 5
A child is sitting on the outer edge of a merry-go-round that is 18 m in diameter. If the merry-go-round makes 4.9 rev/min, what is the velocity of the child in m/s?
- A. 4.6 m/s
- B. 3.2 m/s
- C. 0.7 m/s
- D. 9.2 m/s
**Instructions:** Click Save and Submit to save and submit. Click Save All Answers to save all answers.
---
### Explanation:
To calculate the velocity, we need to use the formula for the linear velocity of an object in circular motion:
\[ v = r \cdot \omega \]
Where:
- \( v \) is the linear velocity.
- \( r \) is the radius of the circular path.
- \( \omega \) is the angular velocity in radians per second.
1. First, find the radius of the merry-go-round:
\[ r = \frac{\text{diameter}}{2} = \frac{18\, \text{m}}{2} = 9\, \text{m} \]
2. Convert the angular velocity from revolutions per minute to radians per second:
\[ 4.9\, \text{rev/min} \cdot \frac{2\pi\, \text{radians}}{1\, \text{rev}} \cdot \frac{1\, \text{min}}{60\, \text{s}} = 4.9 \cdot \frac{2\pi}{60} \, \text{rad/s} \]
3. Calculate the angular velocity:
\[ \omega = 4.9 \cdot \frac{\pi}{30} \approx 0.514\, \text{rad/s} \]
4. Now calculate the linear velocity:
\[ v = r \cdot \omega = 9\, \text{m} \cdot 0.514\, \text{rad/s} \approx 4.63\, \text{m/s} \]
Therefore, the correct answer is:
- **A. 4.6 m/s**
Note: While the detailed explanation provides insight into how the velocity is computed, students are encouraged to practice solving these steps to enhance their understanding of circular motion and angular velocity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8689a897-6f19-4f8c-bce2-bc1e854b9491%2F559a1343-91d8-43d2-b02b-3956aa46938b%2F5qicvu.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 5
A child is sitting on the outer edge of a merry-go-round that is 18 m in diameter. If the merry-go-round makes 4.9 rev/min, what is the velocity of the child in m/s?
- A. 4.6 m/s
- B. 3.2 m/s
- C. 0.7 m/s
- D. 9.2 m/s
**Instructions:** Click Save and Submit to save and submit. Click Save All Answers to save all answers.
---
### Explanation:
To calculate the velocity, we need to use the formula for the linear velocity of an object in circular motion:
\[ v = r \cdot \omega \]
Where:
- \( v \) is the linear velocity.
- \( r \) is the radius of the circular path.
- \( \omega \) is the angular velocity in radians per second.
1. First, find the radius of the merry-go-round:
\[ r = \frac{\text{diameter}}{2} = \frac{18\, \text{m}}{2} = 9\, \text{m} \]
2. Convert the angular velocity from revolutions per minute to radians per second:
\[ 4.9\, \text{rev/min} \cdot \frac{2\pi\, \text{radians}}{1\, \text{rev}} \cdot \frac{1\, \text{min}}{60\, \text{s}} = 4.9 \cdot \frac{2\pi}{60} \, \text{rad/s} \]
3. Calculate the angular velocity:
\[ \omega = 4.9 \cdot \frac{\pi}{30} \approx 0.514\, \text{rad/s} \]
4. Now calculate the linear velocity:
\[ v = r \cdot \omega = 9\, \text{m} \cdot 0.514\, \text{rad/s} \approx 4.63\, \text{m/s} \]
Therefore, the correct answer is:
- **A. 4.6 m/s**
Note: While the detailed explanation provides insight into how the velocity is computed, students are encouraged to practice solving these steps to enhance their understanding of circular motion and angular velocity.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON