The problem involves a disk rolling without slipping on a horizontal surface. At the given moment, the center \( O \) of the disk has a velocity \( v_0 = 3.6 \, \text{m/s} \) and an acceleration \( a_0 = 4.9 \, \text{m/s}^2 \) in the directions indicated in the figure. At this instant, particle \( A \) on the disk has a speed \( u = 1.9 \, \text{m/s} \) and a rate of change of speed \( \dot{u} = 7.1 \, \text{m/s}^2 \), both relative to the disk, in the directions shown.The diagram shows:- A large circle representing the disk with center \( O \).- The x-axis is horizontal, and the y-axis is vertical.- Point \( A \) is located within the disk's upper hemisphere.- \( OA = 0.47 \, \text{m} \) (radius from the center to point A).- \( O \) has given velocity and acceleration.- Vectors show directions of motion: \( v_0 \) along the positive x-axis, \( u \) horizontally towards the left, and acceleration components.You are tasked with determining the absolute velocity \( v_A \) and acceleration \( a_A \) of particle \( A \).**Answers:**- Absolute velocity of particle \( A \): \[ v_A = (-4.34 \, i + 0.00 \, j) \, \text{m/s} \]- Absolute acceleration of particle \( A \): \[ a_A = (1.40 \, i - 1.15 \, j) \, \text{m/s}^2 \]

From the given data and figure,V0 = -3.6 m/s a0 = 4.9 m/s2u = 1.9 m/s = 7.1 m/s2The radius of the wheel, r = 0.64 mThe distance of OA, L = 0.47 mThe angular velocity,

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Mechanical Engineering

The disk rolls without slipping on the horizontal surface, and at the instant represented, the center O has the velocity vo = 3.6 m/s and acceleration ao = 4.9 m/s2 with directions shown in the figure. For this instant, the particle A has the indicated speed u = 1.9 m/s and time rate of change of speed u = 7.1 m/s², both relative to the disk with directions shown in the figure. Determine the absolute velocity VA and acceleration aд of particle A.

The disk rolls without slipping on the horizontal surface, and at the instant represented, the center O has the velocity vo = 3.6 m/s and acceleration ao = 4.9 m/s2 with directions shown in the figure. For this instant, the particle A has the indicated speed u = 1.9 m/s and time rate of change of speed u = 7.1 m/s², both relative to the disk with directions shown in the figure. Determine the absolute velocity VA and acceleration aд of particle A.

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

The problem involves a disk rolling without slipping on a horizontal surface. At the given moment, the center \( O \) of the disk has a velocity \( v_0 = 3.6 \, \text{m/s} \) and an acceleration \( a_0 = 4.9 \, \text{m/s}^2 \) in the directions indicated in the figure. At this instant, particle \( A \) on the disk has a speed \( u = 1.9 \, \text{m/s} \) and a rate of change of speed \( \dot{u} = 7.1 \, \text{m/s}^2 \), both relative to the disk, in the directions shown.

The diagram shows:
- A large circle representing the disk with center \( O \).
- The x-axis is horizontal, and the y-axis is vertical.
- Point \( A \) is located within the disk's upper hemisphere.
- \( OA = 0.47 \, \text{m} \) (radius from the center to point A).
- \( O \) has given velocity and acceleration.
- Vectors show directions of motion: \( v_0 \) along the positive x-axis, \( u \) horizontally towards the left, and acceleration components.

You are tasked with determining the absolute velocity \( v_A \) and acceleration \( a_A \) of particle \( A \).

**Answers:**
- Absolute velocity of particle \( A \):
\[
v_A = (-4.34 \, i + 0.00 \, j) \, \text{m/s}
\]

- Absolute acceleration of particle \( A \):
\[
a_A = (1.40 \, i - 1.15 \, j) \, \text{m/s}^2
\]

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