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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Question
The top point on a 64-cm-diameter rolling bicycle wheel has an instantaneous speed of 14 m/s.
![### Topic: Understanding Wheel Revolutions
The problem statement is as follows:
- The top point on a 64-cm-diameter rolling bicycle wheel has an instantaneous speed of 14 m/s.
#### Part A
**Question:**
How many revolutions will the wheel make in 13 seconds?
**Task:**
Express your answer in revolutions.
#### Solution Approach
To solve this problem, you will need to use the formula relating the circumference of the wheel to the distance traveled and the number of revolutions. Here's the process:
1. **Find the circumference of the wheel:**
The circumference \( C \) is given by the formula:
\[
C = \pi \times \text{diameter}
\]
Given the diameter is 64 cm, convert it to meters (0.64 m for unit consistency).
2. **Calculate the distance traveled:**
The distance \( D \) traveled in 13 seconds can be found using:
\[
D = \text{speed} \times \text{time} = 14 \, \text{m/s} \times 13 \, \text{s}
\]
3. **Determine the number of revolutions \( N \):**
The number of revolutions is the distance traveled divided by the circumference:
\[
N = \frac{D}{C}
\]
This task involves understanding the relationship between linear and rotational motion, and practicing unit conversions and calculations of circular metrics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7cf2af7a-a1e1-4cba-b7ac-6991a1c49765%2F3a15564e-a56c-4dbd-b825-d5603626a303%2Fnuvaw7u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Topic: Understanding Wheel Revolutions
The problem statement is as follows:
- The top point on a 64-cm-diameter rolling bicycle wheel has an instantaneous speed of 14 m/s.
#### Part A
**Question:**
How many revolutions will the wheel make in 13 seconds?
**Task:**
Express your answer in revolutions.
#### Solution Approach
To solve this problem, you will need to use the formula relating the circumference of the wheel to the distance traveled and the number of revolutions. Here's the process:
1. **Find the circumference of the wheel:**
The circumference \( C \) is given by the formula:
\[
C = \pi \times \text{diameter}
\]
Given the diameter is 64 cm, convert it to meters (0.64 m for unit consistency).
2. **Calculate the distance traveled:**
The distance \( D \) traveled in 13 seconds can be found using:
\[
D = \text{speed} \times \text{time} = 14 \, \text{m/s} \times 13 \, \text{s}
\]
3. **Determine the number of revolutions \( N \):**
The number of revolutions is the distance traveled divided by the circumference:
\[
N = \frac{D}{C}
\]
This task involves understanding the relationship between linear and rotational motion, and practicing unit conversions and calculations of circular metrics.
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