### Problem Statement:The center \(O\) of the disk has the velocity and acceleration shown in the figure. If the disk rolls without slipping on the horizontal surface, determine the velocity of \(A\) and the acceleration of \(B\) for the instant represented.### Given data:- \( a = 6.5 \, \text{m/s}^2 \)- \( v = 2.3 \, \text{m/s} \)- \( b = 0.4 \, \text{m} \)- \( \theta = 40^\circ \)### Diagram Explanation:- The figure displays a circular disk rolling horizontally without slipping.- Point \(O\) represents the center of the disk.- \(A\) and \(B\) are points at different positions on the disk.- \(O\) is offset from point \(B\) by a distance \(b\), both on the x-axis and y-axis.- The angle \(\theta\) is formed between point \(A\), \(O\), and the horizontal axis.**Coordinate System:**- An \(x-y\) coordinate axis is indicated, with \(x\) being the horizontal axis and \(y\) the vertical axis.### Answers:**Velocity of \(A\) (\( v_A \)):**\[ v_A = \left( \quad \right) \hat{i} + \left( \quad \right) \hat{j} \, \text{m/s} \]**Acceleration of \(B\) (\( a_B \)):**\[ a_B = \left( \quad \right) \hat{i} + \left( \quad \right) \hat{j} \, \text{m/s}^2 \]Placeholders indicate where students are expected to input or calculate the respective components of velocity and acceleration.

Answered: Image /qna-images/answer/d6c368a7-4331-4125-9501-3f37a23164df.jpg

The center O of the disk has the velocity and acceleration shown in the figure. If the disk rolls without slipping on the horizontal surface, determine the velocity of A and the acceleration of B for the instant represented. Assume a = 6.5 m/s², v= 2.3 m/s, b = 0.4 m, 0 = 40°. a V Answers: VA = (i j) m/s ав= (i j) m/s² i+ i i+ i 1

The center O of the disk has the velocity and acceleration shown in the figure. If the disk rolls without slipping on the horizontal surface, determine the velocity of A and the acceleration of B for the instant represented. Assume a = 6.5 m/s², v= 2.3 m/s, b = 0.4 m, 0 = 40°. a V Answers: VA = (i j) m/s ав= (i j) m/s² i+ i i+ i 1

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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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

### Problem Statement:

The center \(O\) of the disk has the velocity and acceleration shown in the figure. If the disk rolls without slipping on the horizontal surface, determine the velocity of \(A\) and the acceleration of \(B\) for the instant represented.

### Given data:
- \( a = 6.5 \, \text{m/s}^2 \)
- \( v = 2.3 \, \text{m/s} \)
- \( b = 0.4 \, \text{m} \)
- \( \theta = 40^\circ \)

### Diagram Explanation:
- The figure displays a circular disk rolling horizontally without slipping.
- Point \(O\) represents the center of the disk.
- \(A\) and \(B\) are points at different positions on the disk.
- \(O\) is offset from point \(B\) by a distance \(b\), both on the x-axis and y-axis.
- The angle \(\theta\) is formed between point \(A\), \(O\), and the horizontal axis.

**Coordinate System:**
- An \(x-y\) coordinate axis is indicated, with \(x\) being the horizontal axis and \(y\) the vertical axis.

### Answers:

**Velocity of \(A\) (\( v_A \)):**
\[ v_A = \left( \quad \right) \hat{i} + \left( \quad \right) \hat{j} \, \text{m/s} \]

**Acceleration of \(B\) (\( a_B \)):**
\[ a_B = \left( \quad \right) \hat{i} + \left( \quad \right) \hat{j} \, \text{m/s}^2 \]

Placeholders indicate where students are expected to input or calculate the respective components of velocity and acceleration.

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