Consider the disk in (Figure 1). The angular acceleration of the disk is defined by a = (3t² + 16) rad/s², where t is in seconds. The disk is originally rotating at wo = 16 rad/s. Figure A 0.8 m < 1 of 1 > Part A Determine the magnitude of the velocity of point A on the disk when t = 2 s. Express your answer in meters per second to three significant figures. 17 ΑΣΦ VA = Submit Previous Answers Request Answer X Incorrect; Try Again Part B vec (a)n. (as)t Determine the magnitudes of the n and t components of acceleration of point A on the disk when t = 2 s. = Express your answers in meters per square second using three significant figures separated by a comma. Π| ΑΣΦ | | ? vec 6 m/s Submit Previous Answers Request Answer ? m/s²

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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**Educational Content: Rotational Motion and Angular Acceleration**

**Introduction**

Consider a disk as shown in the accompanying diagram. The angular acceleration \(\alpha\) of the disk is defined by the equation:

\[
\alpha = (3t^2 + 16) \, \text{rad/s}^2
\]

where \(t\) is the time in seconds. The disk begins with an initial angular velocity \(\omega_0 = 16 \, \text{rad/s}\).

**Diagram Explanation**

The diagram illustrates a disk with a point \(A\) located on its edge, 0.8 meters from the center. The disk is rotating in a clockwise direction as indicated by the blue arrow.

**Problem Solving**

### Part A

**Objective:**  
Determine the magnitude of the velocity of point \(A\) on the disk at \(t = 2 \, \text{s}\).

- **Input Required:**  
  Express your answer in meters per second to three significant figures.

- **Current Status:**  
  The answer given was incorrect, prompting a retry.

### Part B

**Objective:**  
Determine the magnitudes of the normal (n) and tangential (t) components of acceleration of point \(A\) on the disk at \(t = 2 \, \text{s}\).

- **Input Required:**  
  Express your answers in meters per square second, separated by a comma, using three significant figures.

The interface provides input fields to submit answers. Users can refer to previous attempts or request hints if needed.

**Conclusion**

This exercise requires understanding concepts like rotational kinematics, specifically angular acceleration and its effect on the velocity and acceleration components of rotating bodies. Solving this will enhance comprehension of dynamic systems in physics.
Transcribed Image Text:**Educational Content: Rotational Motion and Angular Acceleration** **Introduction** Consider a disk as shown in the accompanying diagram. The angular acceleration \(\alpha\) of the disk is defined by the equation: \[ \alpha = (3t^2 + 16) \, \text{rad/s}^2 \] where \(t\) is the time in seconds. The disk begins with an initial angular velocity \(\omega_0 = 16 \, \text{rad/s}\). **Diagram Explanation** The diagram illustrates a disk with a point \(A\) located on its edge, 0.8 meters from the center. The disk is rotating in a clockwise direction as indicated by the blue arrow. **Problem Solving** ### Part A **Objective:** Determine the magnitude of the velocity of point \(A\) on the disk at \(t = 2 \, \text{s}\). - **Input Required:** Express your answer in meters per second to three significant figures. - **Current Status:** The answer given was incorrect, prompting a retry. ### Part B **Objective:** Determine the magnitudes of the normal (n) and tangential (t) components of acceleration of point \(A\) on the disk at \(t = 2 \, \text{s}\). - **Input Required:** Express your answers in meters per square second, separated by a comma, using three significant figures. The interface provides input fields to submit answers. Users can refer to previous attempts or request hints if needed. **Conclusion** This exercise requires understanding concepts like rotational kinematics, specifically angular acceleration and its effect on the velocity and acceleration components of rotating bodies. Solving this will enhance comprehension of dynamic systems in physics.
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