Up Left + Right Down A spinning disk is rotating at a rate of 5 rad/s in the positive counterclock-wise direction. If the disk is subjected to an angular acceleration in the counterclock-wise direction at a rate of 4 rad/s², Find the wheel's angular velocity in rad/s after 4 s. 11 rad/s. -16 rad/s. -11 rad/s. 21 rad/s. -21 rad/s.
Up Left + Right Down A spinning disk is rotating at a rate of 5 rad/s in the positive counterclock-wise direction. If the disk is subjected to an angular acceleration in the counterclock-wise direction at a rate of 4 rad/s², Find the wheel's angular velocity in rad/s after 4 s. 11 rad/s. -16 rad/s. -11 rad/s. 21 rad/s. -21 rad/s.
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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![**Problem Statement:**
A spinning disk is rotating at a rate of 5 rad/s in the positive counterclockwise direction. If the disk is subjected to an angular acceleration in the counterclockwise direction at a rate of 4 rad/s², find the wheel's angular velocity in rad/s after 4 seconds.
**Diagram Explanation:**
The image contains two main components:
1. **Spinning Disk Illustration:**
- An oval shape represents the top view of a spinning disk.
- A directional arrow around the disk indicates counterclockwise rotation.
2. **Coordinate Directions:**
- An arrow diagram showing "Left," "Right," "Up," and "Down" directions.
**Answer Options:**
- ○ 11 rad/s
- ○ 16 rad/s
- ○ -11 rad/s
- ○ 21 rad/s
- ○ -21 rad/s
**Solution Approach:**
To determine the angular velocity of the disk after 4 seconds, use the formula:
\[
\omega = \omega_0 + \alpha \cdot t
\]
Where:
- \(\omega\) is the final angular velocity.
- \(\omega_0 = 5 \, \text{rad/s}\) is the initial angular velocity.
- \(\alpha = 4 \, \text{rad/s}^2\) is the angular acceleration.
- \(t = 4 \, \text{s}\) is the time duration.
\[
\omega = 5 \, \text{rad/s} + (4 \, \text{rad/s}^2 \times 4 \, \text{s}) = 5 \, \text{rad/s} + 16 \, \text{rad/s} = 21 \, \text{rad/s}
\]
**Correct Answer:**
- ○ 21 rad/s](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45d57c72-fda0-4c9d-b683-c1e77ae3201f%2Fe87f3873-92ea-4f0e-8093-cc032dcdf634%2Fdri8y0n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A spinning disk is rotating at a rate of 5 rad/s in the positive counterclockwise direction. If the disk is subjected to an angular acceleration in the counterclockwise direction at a rate of 4 rad/s², find the wheel's angular velocity in rad/s after 4 seconds.
**Diagram Explanation:**
The image contains two main components:
1. **Spinning Disk Illustration:**
- An oval shape represents the top view of a spinning disk.
- A directional arrow around the disk indicates counterclockwise rotation.
2. **Coordinate Directions:**
- An arrow diagram showing "Left," "Right," "Up," and "Down" directions.
**Answer Options:**
- ○ 11 rad/s
- ○ 16 rad/s
- ○ -11 rad/s
- ○ 21 rad/s
- ○ -21 rad/s
**Solution Approach:**
To determine the angular velocity of the disk after 4 seconds, use the formula:
\[
\omega = \omega_0 + \alpha \cdot t
\]
Where:
- \(\omega\) is the final angular velocity.
- \(\omega_0 = 5 \, \text{rad/s}\) is the initial angular velocity.
- \(\alpha = 4 \, \text{rad/s}^2\) is the angular acceleration.
- \(t = 4 \, \text{s}\) is the time duration.
\[
\omega = 5 \, \text{rad/s} + (4 \, \text{rad/s}^2 \times 4 \, \text{s}) = 5 \, \text{rad/s} + 16 \, \text{rad/s} = 21 \, \text{rad/s}
\]
**Correct Answer:**
- ○ 21 rad/s
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