**Part C**Determine the angular acceleration of the disk when \( t = 85 \, \text{s} \), measured counterclockwise.Express your answer in radians per second squared to three significant figures. Enter a positive value if the angular acceleration is counterclockwise and a negative value if the angular acceleration is clockwise.---### Input Box for Answer:- \( \alpha = \) \(\_\_\_\_\_\_\_\_\_\_\_\) \(\text{rad/s}^2\)### Explanation:- The section includes a text box where users can enter their answers.- Use the input interface to submit the calculated angular acceleration value, adhering to the required precision and unit specifications.### Context:- This task is designed for educational purposes to assess understanding of angular motion, specifically angular acceleration, through numerical computation. **Educational Content: Analyzing Rotational Motion****Overview:**This educational exercise involves analyzing the rotational motion of a disk driven by a motor. The angular position of the disk, denoted as \(\theta\), is expressed by the equation:\[ \theta = (20t + 4t^2) \, \text{rad} \]where \( t \) is the time in seconds.**Figure Description:**The figure illustrates a motor connected to a disk. The motor drives the disk, and the distance from the motor's center to the edge of the disk is labeled as 0.5 ft. The disk's rotational angle is represented by \(\theta\).**Problem-Solving Steps:****Part A:**- **Objective:** Determine the number of revolutions completed by the disk at \( t = 85 \) seconds.- **Instructions:** Express your answer in revolutions to three significant figures.- **Input Format:** Use the box provided to enter your answer in rev (revolutions).**Part B:**- **Objective:** Calculate the angular velocity of the disk at \( t = 85 \) seconds, with the direction measured counterclockwise.- **Instructions:** Express your answer in radians per second to three significant figures. A positive value indicates counterclockwise rotation, while a negative value indicates clockwise rotation.- **Input Format:** Use the box provided to enter your angular velocity in rad/s.This exercise requires understanding of angular kinematics to solve for rotational parameters from given equations. Ensure familiarity with converting angles from radians to revolutions and calculating angular velocity.

We will compute the number of rotations of the disk using the angular velocity and angular…

The disk is driven by a motor such that the angular position of the disk is defined by 0 = (20t+4+²) rad, where t is in seconds. (Figure 1) Part A Determine the number of revolutions of the disk when t = 85 s. Express your answer in revolutions to three significant figures. 15. ΑΣΦ 41 vec Submit Previous Answers Request Answer 2 ? rev

The disk is driven by a motor such that the angular position of the disk is defined by 0 = (20t+4+²) rad, where t is in seconds. (Figure 1) Part A Determine the number of revolutions of the disk when t = 85 s. Express your answer in revolutions to three significant figures. 15. ΑΣΦ 41 vec Submit Previous Answers Request Answer 2 ? rev

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

**Part C**

Determine the angular acceleration of the disk when \( t = 85 \, \text{s} \), measured counterclockwise.

Express your answer in radians per second squared to three significant figures. Enter a positive value if the angular acceleration is counterclockwise and a negative value if the angular acceleration is clockwise.

---

### Input Box for Answer:
- \( \alpha = \) \(\_\_\_\_\_\_\_\_\_\_\_\) \(\text{rad/s}^2\)

### Explanation:
- The section includes a text box where users can enter their answers.
- Use the input interface to submit the calculated angular acceleration value, adhering to the required precision and unit specifications.

### Context:
- This task is designed for educational purposes to assess understanding of angular motion, specifically angular acceleration, through numerical computation.

**Educational Content: Analyzing Rotational Motion**

**Overview:**
This educational exercise involves analyzing the rotational motion of a disk driven by a motor. The angular position of the disk, denoted as \(\theta\), is expressed by the equation:
\[ \theta = (20t + 4t^2) \, \text{rad} \]
where \( t \) is the time in seconds.

**Figure Description:**
The figure illustrates a motor connected to a disk. The motor drives the disk, and the distance from the motor's center to the edge of the disk is labeled as 0.5 ft. The disk's rotational angle is represented by \(\theta\).

**Problem-Solving Steps:**

**Part A:**
- **Objective:** Determine the number of revolutions completed by the disk at \( t = 85 \) seconds.
- **Instructions:** Express your answer in revolutions to three significant figures.
- **Input Format:** Use the box provided to enter your answer in rev (revolutions).

**Part B:**
- **Objective:** Calculate the angular velocity of the disk at \( t = 85 \) seconds, with the direction measured counterclockwise.
- **Instructions:** Express your answer in radians per second to three significant figures. A positive value indicates counterclockwise rotation, while a negative value indicates clockwise rotation.
- **Input Format:** Use the box provided to enter your angular velocity in rad/s.

This exercise requires understanding of angular kinematics to solve for rotational parameters from given equations. Ensure familiarity with converting angles from radians to revolutions and calculating angular velocity.

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Step 2: Calculation of the number of revolutions of the disk:

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Step 3: Calculation of angular velocity and angular acceleration of the disk:

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