### Angular Motion of a Circular Disk**Problem Statement:**Point A of the circular disk is at the angular position \(\theta = 0\) at time \(t = 0\). The disk has an angular velocity \(\omega_0 = 0.29 \text{ rad/s}\) at \(t = 0\) and subsequently experiences an angular acceleration \(\alpha = 1.8t\) where \(t\) is in seconds, and \(\alpha\) is in radians per second squared. Determine the velocity and acceleration of point A in terms of fixed \(i\) and \(j\) unit vectors at time \(t = 2.7 \text{ s}\).**Assumptions:**- \( r = 145 \text{ mm} \)**Diagram Explanation:**The provided diagram represents a circular disk with point A located on the periphery of the disk. The angular acceleration \(\alpha\) is indicated at the center of the rotation, and the disk is rotating in the counterclockwise direction. The \(x\) and \(y\) axes or the fixed coordinates system are also shown. The position of point A is specified with angle \(\theta\) from the reference axis.**Answers:**### Velocity and Acceleration Computations:\[ v_A = \left( \boxed{0} \right) i + \left( \boxed{1} \right) j \text{ m/s} \]\[ a_A = \left( \boxed{6.806} \right) i + \left( \boxed{0.705} \right) j \text{ m/s}^2 \]In the above solutions:- \( v_A \) denotes the velocity of point A in the fixed coordinates.- \( a_A \) denotes the acceleration of point A in the fixed coordinates.- \(i\) and \(j\) represent the unit vectors in the \(x\) and \(y\) directions, respectively.

Answered: Image /qna-images/answer/655ae866-98e0-43f6-8792-8e14ddd707fd.jpg

Point A of the circular disk is at the angular position 0 = 0 at time t = 0. The disk has angular velocity wo = 0.29 rad/s at t = 0 and subsequently experiences an angular acceleration a = 1.8t where t is in seconds, and a is in radians per second squared. Determine the velocity and acceleration of point A in terms of fixed i and j unit vectors at time t = 2.7 s.

Point A of the circular disk is at the angular position 0 = 0 at time t = 0. The disk has angular velocity wo = 0.29 rad/s at t = 0 and subsequently experiences an angular acceleration a = 1.8t where t is in seconds, and a is in radians per second squared. Determine the velocity and acceleration of point A in terms of fixed i and j unit vectors at time t = 2.7 s.

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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Question

### Angular Motion of a Circular Disk

**Problem Statement:**

Point A of the circular disk is at the angular position \(\theta = 0\) at time \(t = 0\). The disk has an angular velocity \(\omega_0 = 0.29 \text{ rad/s}\) at \(t = 0\) and subsequently experiences an angular acceleration \(\alpha = 1.8t\) where \(t\) is in seconds, and \(\alpha\) is in radians per second squared. Determine the velocity and acceleration of point A in terms of fixed \(i\) and \(j\) unit vectors at time \(t = 2.7 \text{ s}\).

**Assumptions:**

- \( r = 145 \text{ mm} \)

**Diagram Explanation:**

The provided diagram represents a circular disk with point A located on the periphery of the disk. The angular acceleration \(\alpha\) is indicated at the center of the rotation, and the disk is rotating in the counterclockwise direction. The \(x\) and \(y\) axes or the fixed coordinates system are also shown. The position of point A is specified with angle \(\theta\) from the reference axis.

**Answers:**

### Velocity and Acceleration Computations:

\[ v_A = \left( \boxed{0} \right) i + \left( \boxed{1} \right) j \text{ m/s} \]

\[ a_A = \left( \boxed{6.806} \right) i + \left( \boxed{0.705} \right) j \text{ m/s}^2 \]

In the above solutions:
- \( v_A \) denotes the velocity of point A in the fixed coordinates.
- \( a_A \) denotes the acceleration of point A in the fixed coordinates.
- \(i\) and \(j\) represent the unit vectors in the \(x\) and \(y\) directions, respectively.

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