** Educational Content: Understanding Angular Velocity in Rotational Systems ****Problem Context:**The scenario involves a vacuum cleaner’s armature shaft, denoted as shaft \( S \) in the illustration (Figure 1). This shaft rotates with an angular acceleration defined by the equation:\[ \alpha = -4\omega^{3/4} \,\, \text{rad/s}^2 \]where \( \omega \) is the angular velocity in radians per second (rad/s).**Task (Part A):**We need to determine the angular velocity of the brush at time \( t = 5 \, \text{s} \). The process begins from an initial angular velocity \( \omega_0 = 1.0 \, \text{rad/s} \), at \( t = 0 \). The problem specifies the radii of the shaft and the brush as 0.35 inches and 1.1 inches respectively. Importantly, any thickness from the drive belt should be neglected in calculations.**Required Expression:**Express the final answer in radians per second, ensuring that the result is accurate to three significant figures.**User Input:**The user has attempted to calculate the final angular velocity, submitting a value of \( \omega_B = 156 \, \text{rad/s} \), which was marked incorrect. The system indicates that four additional attempts remain for further submissions.**Visual Aid: Figure Explanation:**The figure displays an illustration of a vacuum cleaner, highlighting the critical components, including the armature shaft and brush. This visual representation helps in understanding the mechanical setup pertinent to solving the angular velocity problem.For any assistance or additional hints, users can click on the "View Available Hint(s)" option. Remember, accurate problem-solving includes reconsidering the calculations, understanding the role of negative angular acceleration, and the relationship between angular velocity and time.

Given data: α=4ω3/4t=5 sωi=1 rad/s The angular velocity of the brush is needed to be determined.

Answered: The vacuum cleaner's armature shaft S…

The vacuum cleaner's armature shaft S shown in (Eigure 1) rotates with an angular acceleration of a-4³/4 rad/s², where w is in rad/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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Concept explainers

Basic Terminology in Mechanics

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its environment. This branch of physics keeps its roots in Ancient Greece in the form of the scripts of Aristotle and Archimedes.

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** Educational Content: Understanding Angular Velocity in Rotational Systems **

**Problem Context:**

The scenario involves a vacuum cleaner’s armature shaft, denoted as shaft \( S \) in the illustration (Figure 1). This shaft rotates with an angular acceleration defined by the equation:

\[ \alpha = -4\omega^{3/4} \,\, \text{rad/s}^2 \]

where \( \omega \) is the angular velocity in radians per second (rad/s).

**Task (Part A):**

We need to determine the angular velocity of the brush at time \( t = 5 \, \text{s} \). The process begins from an initial angular velocity \( \omega_0 = 1.0 \, \text{rad/s} \), at \( t = 0 \). The problem specifies the radii of the shaft and the brush as 0.35 inches and 1.1 inches respectively. Importantly, any thickness from the drive belt should be neglected in calculations.

**Required Expression:**

Express the final answer in radians per second, ensuring that the result is accurate to three significant figures.

**User Input:**

The user has attempted to calculate the final angular velocity, submitting a value of \( \omega_B = 156 \, \text{rad/s} \), which was marked incorrect. The system indicates that four additional attempts remain for further submissions.

**Visual Aid: Figure Explanation:**

The figure displays an illustration of a vacuum cleaner, highlighting the critical components, including the armature shaft and brush. This visual representation helps in understanding the mechanical setup pertinent to solving the angular velocity problem.

For any assistance or additional hints, users can click on the "View Available Hint(s)" option.

Remember, accurate problem-solving includes reconsidering the calculations, understanding the role of negative angular acceleration, and the relationship between angular velocity and time.

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