A bicycle with 20-inch diameter wheels is traveling at 17 mi/h. Find the angular speed of the wheels in rad/min. Enter the exact answer. W = Number rad/min How many revolutions per minute do the wheels make? Round your answer to three decimal places. The wheels make Number revolutions per minute.
A bicycle with 20-inch diameter wheels is traveling at 17 mi/h. Find the angular speed of the wheels in rad/min. Enter the exact answer. W = Number rad/min How many revolutions per minute do the wheels make? Round your answer to three decimal places. The wheels make Number revolutions per minute.
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![### Problem Statement
A bicycle with 20-inch diameter wheels is traveling at 17 mi/h.
**Task 1:**
Find the angular speed of the wheels in radians per minute (rad/min).
Enter the exact answer in the space provided.
- \(\omega =\) [Enter Number] rad/min
**Task 2:**
How many revolutions per minute do the wheels make?
Round your answer to three decimal places.
- The wheels make [Enter Number] revolutions per minute.
### Explanation
To solve these problems, you need to apply concepts from circular motion and conversions between linear and angular velocity.
#### Concepts Involved:
1. **Angular Speed (\(\omega\)):**
- Angular speed is the rate at which the angle changes with respect to time.
- \(\omega = \frac{v}{r}\), where \(v\) is the linear speed and \(r\) is the radius of the wheel.
2. **Conversions:**
- 1 mile = 5280 feet
- 1 hour = 60 minutes
- 1 revolution = \(2\pi\) radians
3. **Revolutions Per Minute (RPM):**
- RPM can be calculated by dividing the angular speed by \(2\pi\).
### Calculation Steps
1. **Convert Linear Speed to Feet per Minute:**
- \(17 \, \text{mi/h} = 17 \times 5280 \, \text{ft/h} = 17 \times 5280 / 60 \, \text{ft/min}\)
2. **Calculate Angular Speed:**
- Radius, \(r\), is half of the diameter, so \(r = 10\) inches = \(10/12\) feet.
- \(\omega = \frac{v}{r}\) in rad/min.
3. **Convert Angular Speed to RPM:**
- Divide the angular speed by \(2\pi\).
These calculations will provide the necessary values to complete the tasks outlined.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F466aa07a-ac9f-45f8-bdd3-e5db76dbf63c%2F1930f009-c50f-4c5b-bb12-9212c9333200%2Fjpno0qr_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A bicycle with 20-inch diameter wheels is traveling at 17 mi/h.
**Task 1:**
Find the angular speed of the wheels in radians per minute (rad/min).
Enter the exact answer in the space provided.
- \(\omega =\) [Enter Number] rad/min
**Task 2:**
How many revolutions per minute do the wheels make?
Round your answer to three decimal places.
- The wheels make [Enter Number] revolutions per minute.
### Explanation
To solve these problems, you need to apply concepts from circular motion and conversions between linear and angular velocity.
#### Concepts Involved:
1. **Angular Speed (\(\omega\)):**
- Angular speed is the rate at which the angle changes with respect to time.
- \(\omega = \frac{v}{r}\), where \(v\) is the linear speed and \(r\) is the radius of the wheel.
2. **Conversions:**
- 1 mile = 5280 feet
- 1 hour = 60 minutes
- 1 revolution = \(2\pi\) radians
3. **Revolutions Per Minute (RPM):**
- RPM can be calculated by dividing the angular speed by \(2\pi\).
### Calculation Steps
1. **Convert Linear Speed to Feet per Minute:**
- \(17 \, \text{mi/h} = 17 \times 5280 \, \text{ft/h} = 17 \times 5280 / 60 \, \text{ft/min}\)
2. **Calculate Angular Speed:**
- Radius, \(r\), is half of the diameter, so \(r = 10\) inches = \(10/12\) feet.
- \(\omega = \frac{v}{r}\) in rad/min.
3. **Convert Angular Speed to RPM:**
- Divide the angular speed by \(2\pi\).
These calculations will provide the necessary values to complete the tasks outlined.
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