A ceiling fan has 17-inch blades (so the radius of the circular fan is 17 inches). Suppose the linear speed of the tip of a blade is 9 feet per second. (a) Find the angular speed of the fan in radians per minute. (b) Find the number of revolutions a blade makes per minute. Do not round any intermediate computations, and round your answer to the nearest whole number. (a) Angular speed:[] radians per minute (b) Number of revolutions per minute:
A ceiling fan has 17-inch blades (so the radius of the circular fan is 17 inches). Suppose the linear speed of the tip of a blade is 9 feet per second. (a) Find the angular speed of the fan in radians per minute. (b) Find the number of revolutions a blade makes per minute. Do not round any intermediate computations, and round your answer to the nearest whole number. (a) Angular speed:[] radians per minute (b) Number of revolutions per minute:
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Chapter1: Units, Trigonometry. And Vectors
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![### Problem Statement:
A ceiling fan has 17-inch blades (so the radius of the circular fan is 17 inches). Suppose the linear speed of the tip of a blade is 9 feet per second.
**(a)** Find the angular speed of the fan in radians per minute.
**(b)** Find the number of revolutions a blade makes per minute.
Do not round any intermediate computations, and round your answer to the nearest whole number.
---
### Provided Information:
- Radius of the fan: 17 inches
- Linear speed of the blade tip: 9 feet per second
### Required Answers:
- (a) Angular speed: ____ radians per minute
- (b) Number of revolutions per minute: ____
### Explanation:
To solve the problem, you first need to note the required angular speed and the number of revolutions per minute based on given information. Here’s a step-by-step guideline to follow:
1. **Convert the radius to feet** (since the linear speed is given in feet per second).
- 1 foot = 12 inches
- Therefore, 17 inches = 17 / 12 feet
2. **Determine the angular speed** using the relationship:
- Linear speed \(v\) = Radius \(r\) x Angular speed \(\omega\)
- Given \(v = 9\) feet/second and \(r = 17/12\) feet.
From \(v = r\omega\):
\[
\omega = \frac{v}{r} = \frac{9 \, \text{feet/second}}{17/12 \, \text{feet}}
\]
- The result will be in radians per second.
3. **Convert the angular speed from seconds to minutes**:
- \(\omega \text{ (minutes)} = \omega \text{ (seconds)} \times 60\)
4. **Determine the number of revolutions per minute**:
- 1 revolution = \(2\pi\) radians
- Therefore, the number of revolutions per minute \(N\) can be found by:
\[
N = \frac{\omega \, \text{(in radians per minute)}}{2\pi}
\]
### Input Answers:
- (a) Angular speed: ____ radians per minute
- (b) Number of revolutions per minute: __](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c0c699c-0ea3-4621-a196-a76a2f333ed8%2F35d087e6-c68b-47d5-b502-83f6c8e078ba%2Fcejyluo_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
A ceiling fan has 17-inch blades (so the radius of the circular fan is 17 inches). Suppose the linear speed of the tip of a blade is 9 feet per second.
**(a)** Find the angular speed of the fan in radians per minute.
**(b)** Find the number of revolutions a blade makes per minute.
Do not round any intermediate computations, and round your answer to the nearest whole number.
---
### Provided Information:
- Radius of the fan: 17 inches
- Linear speed of the blade tip: 9 feet per second
### Required Answers:
- (a) Angular speed: ____ radians per minute
- (b) Number of revolutions per minute: ____
### Explanation:
To solve the problem, you first need to note the required angular speed and the number of revolutions per minute based on given information. Here’s a step-by-step guideline to follow:
1. **Convert the radius to feet** (since the linear speed is given in feet per second).
- 1 foot = 12 inches
- Therefore, 17 inches = 17 / 12 feet
2. **Determine the angular speed** using the relationship:
- Linear speed \(v\) = Radius \(r\) x Angular speed \(\omega\)
- Given \(v = 9\) feet/second and \(r = 17/12\) feet.
From \(v = r\omega\):
\[
\omega = \frac{v}{r} = \frac{9 \, \text{feet/second}}{17/12 \, \text{feet}}
\]
- The result will be in radians per second.
3. **Convert the angular speed from seconds to minutes**:
- \(\omega \text{ (minutes)} = \omega \text{ (seconds)} \times 60\)
4. **Determine the number of revolutions per minute**:
- 1 revolution = \(2\pi\) radians
- Therefore, the number of revolutions per minute \(N\) can be found by:
\[
N = \frac{\omega \, \text{(in radians per minute)}}{2\pi}
\]
### Input Answers:
- (a) Angular speed: ____ radians per minute
- (b) Number of revolutions per minute: __
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