Review A wheel on an indoor exercise bike (a spinning bike) accelerates steadily from 130 rpm to 280 rpm in 4.5 s . The radius of the wheel is 42 cm . Part B Determine the radial component of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. Don't forget that the wheel has an initial angular velocity when it started accelerating. Express your answer using two significant figures. ? ar = 1.5 m/s? Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining
Review A wheel on an indoor exercise bike (a spinning bike) accelerates steadily from 130 rpm to 280 rpm in 4.5 s . The radius of the wheel is 42 cm . Part B Determine the radial component of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. Don't forget that the wheel has an initial angular velocity when it started accelerating. Express your answer using two significant figures. ? ar = 1.5 m/s? Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining
College Physics
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Chapter1: Units, Trigonometry. And Vectors
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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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Topic Video
Question
![**Exercise: Determining Radial Acceleration**
**Problem Statement:**
A wheel on an indoor exercise bike (a spinning bike) accelerates steadily from 130 rpm to 280 rpm in 4.5 seconds. The radius of the wheel is 42 cm.
---
**Part B:**
Determine the radial component of the linear acceleration of a point on the edge of the wheel 2.0 seconds after it has started accelerating. Don't forget that the wheel has an initial angular velocity when it started accelerating.
**Instructions:**
Express your answer using two significant figures.
---
**Student's Answer Entry:**
\[ a_T = \boxed{1.5} \, \text{m/s}^2 \]
**Feedback:**
\[ \text{Incorrect; Try Again; 5 attempts remaining} \]
---
**Explanation of Graphs/Diagrams:**
There are no graphs or diagrams provided in this problem statement. The interface includes a box for entering the answer, a "Submit" button for submitting the answer, options to review previous answers, and a "Request Answer" button, showing an incorrect attempt by the student and the number of attempts remaining.
---
**Note:**
It is important to correctly calculate the radial component of the linear acceleration using the provided parameters and the appropriate equations related to circular motion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33f848af-7ea2-4b7e-a4c9-e1f33a68a6a6%2F973a3131-6a0f-43f9-adf1-8ade61446edc%2Ff3r859j.png&w=3840&q=75)
Transcribed Image Text:**Exercise: Determining Radial Acceleration**
**Problem Statement:**
A wheel on an indoor exercise bike (a spinning bike) accelerates steadily from 130 rpm to 280 rpm in 4.5 seconds. The radius of the wheel is 42 cm.
---
**Part B:**
Determine the radial component of the linear acceleration of a point on the edge of the wheel 2.0 seconds after it has started accelerating. Don't forget that the wheel has an initial angular velocity when it started accelerating.
**Instructions:**
Express your answer using two significant figures.
---
**Student's Answer Entry:**
\[ a_T = \boxed{1.5} \, \text{m/s}^2 \]
**Feedback:**
\[ \text{Incorrect; Try Again; 5 attempts remaining} \]
---
**Explanation of Graphs/Diagrams:**
There are no graphs or diagrams provided in this problem statement. The interface includes a box for entering the answer, a "Submit" button for submitting the answer, options to review previous answers, and a "Request Answer" button, showing an incorrect attempt by the student and the number of attempts remaining.
---
**Note:**
It is important to correctly calculate the radial component of the linear acceleration using the provided parameters and the appropriate equations related to circular motion.
![### Problem Statement
**Scenario:**
A wheel on an indoor exercise bike (a spinning bike) accelerates steadily from 130 rpm to 280 rpm in 4.5 seconds. The radius of the wheel is 42 cm.
**Question:**
Determine the tangential component of the linear acceleration of a point on the edge of the wheel 2.0 seconds after it has started accelerating.
**Instructions:**
Express your answer using two significant figures.
### Calculation
To solve this problem, we need to follow these steps:
1. **Convert rpm to radians per second (rad/s):**
\[
1 \, \text{rpm} = \frac{2\pi}{60} \, \text{rad/s}
\]
- Initial angular velocity (\( \omega_i \)):
\[
130 \, \text{rpm} \times \frac{2\pi}{60} \approx 13.6 \, \text{rad/s}
\]
- Final angular velocity (\( \omega_f \)):
\[
280 \, \text{rpm} \times \frac{2\pi}{60} \approx 29.3 \, \text{rad/s}
\]
2. **Calculate angular acceleration (\( \alpha \)):**
\[
\alpha = \frac{\omega_f - \omega_i}{t}
\]
\[
\alpha = \frac{29.3 \, \text{rad/s} - 13.6 \, \text{rad/s}}{4.5 \, \text{s}} \approx 3.48 \, \text{rad/s}^2
\]
3. **Find angular velocity after 2.0 seconds (\( \omega \)):**
\[
\omega = \omega_i + \alpha t
\]
\[
\omega = 13.6 \, \text{rad/s} + 3.48 \, \text{rad/s}^2 \times 2 \, \text{s} \approx 20.6 \, \text{rad/s}
\]
4. **Determine the tangential acceleration (\( a_t \)):**
\[
a_t = r\alpha
\]
- Radius (\( r \)):
\[](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33f848af-7ea2-4b7e-a4c9-e1f33a68a6a6%2F973a3131-6a0f-43f9-adf1-8ade61446edc%2Fr621kgr.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
**Scenario:**
A wheel on an indoor exercise bike (a spinning bike) accelerates steadily from 130 rpm to 280 rpm in 4.5 seconds. The radius of the wheel is 42 cm.
**Question:**
Determine the tangential component of the linear acceleration of a point on the edge of the wheel 2.0 seconds after it has started accelerating.
**Instructions:**
Express your answer using two significant figures.
### Calculation
To solve this problem, we need to follow these steps:
1. **Convert rpm to radians per second (rad/s):**
\[
1 \, \text{rpm} = \frac{2\pi}{60} \, \text{rad/s}
\]
- Initial angular velocity (\( \omega_i \)):
\[
130 \, \text{rpm} \times \frac{2\pi}{60} \approx 13.6 \, \text{rad/s}
\]
- Final angular velocity (\( \omega_f \)):
\[
280 \, \text{rpm} \times \frac{2\pi}{60} \approx 29.3 \, \text{rad/s}
\]
2. **Calculate angular acceleration (\( \alpha \)):**
\[
\alpha = \frac{\omega_f - \omega_i}{t}
\]
\[
\alpha = \frac{29.3 \, \text{rad/s} - 13.6 \, \text{rad/s}}{4.5 \, \text{s}} \approx 3.48 \, \text{rad/s}^2
\]
3. **Find angular velocity after 2.0 seconds (\( \omega \)):**
\[
\omega = \omega_i + \alpha t
\]
\[
\omega = 13.6 \, \text{rad/s} + 3.48 \, \text{rad/s}^2 \times 2 \, \text{s} \approx 20.6 \, \text{rad/s}
\]
4. **Determine the tangential acceleration (\( a_t \)):**
\[
a_t = r\alpha
\]
- Radius (\( r \)):
\[
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