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TO || rad k

TO || rad k

Elements Of Electromagnetics
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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## Physics Problem: Toilet Paper Roll Angular Acceleration ### Scenario You were able to obtain a roll of toilet paper during quarantine and put it to good use. If the roll rests against a wall where its coefficient of friction is \(\mu_k = 0.22\) and you apply a force of \(0.7 \, \text{N}\) at an angle of 40° from the vertical, determine the angular acceleration of the roll. Mark a counterclockwise acceleration as positive and a clockwise acceleration as negative. Assume the force \(F\) is tangent to the roll. ### Given - Coefficient of friction, \(\mu_k = 0.22\) - Applied force, \(F = 0.7 \, \text{N}\) - Angle of force from the vertical = 40° - Mass of the roll = \(0.21 \, \text{kg}\) - Width of the roll = \(11.5 \, \text{cm}\) - Radius of the roll = \(7.5 \, \text{cm}\) - Distance \(d = -13 \, \text{cm}\) from point A to point B ### Diagram Explanation The diagram presents a vertical cylindrical roll of toilet paper resting against a wall. The point B is at the center of the roll, r denotes the radius of the roll, and F indicates the direction of the force applied at an angle \(\theta\) from the vertical. The point A is on the wall and d signifies the vertical distance from A to B. ### Computation To determine the angular acceleration \(\vec{\alpha}\): \[ \alpha = \boxed{ \frac{}{} \, \hat{k} \, \text{rad} \, \text{s}^{-2} } \] ### Additional Note Hint: Watch your vector direction for \(\vec{\alpha}\) above. --- This problem is a practical application involving the concepts of torque, rotational motion, and the coefficient of friction. Use these fundamentals to solve for the angular acceleration of the toilet paper roll.
Transcribed Image Text:## Physics Problem: Toilet Paper Roll Angular Acceleration ### Scenario You were able to obtain a roll of toilet paper during quarantine and put it to good use. If the roll rests against a wall where its coefficient of friction is \(\mu_k = 0.22\) and you apply a force of \(0.7 \, \text{N}\) at an angle of 40° from the vertical, determine the angular acceleration of the roll. Mark a counterclockwise acceleration as positive and a clockwise acceleration as negative. Assume the force \(F\) is tangent to the roll. ### Given - Coefficient of friction, \(\mu_k = 0.22\) - Applied force, \(F = 0.7 \, \text{N}\) - Angle of force from the vertical = 40° - Mass of the roll = \(0.21 \, \text{kg}\) - Width of the roll = \(11.5 \, \text{cm}\) - Radius of the roll = \(7.5 \, \text{cm}\) - Distance \(d = -13 \, \text{cm}\) from point A to point B ### Diagram Explanation The diagram presents a vertical cylindrical roll of toilet paper resting against a wall. The point B is at the center of the roll, r denotes the radius of the roll, and F indicates the direction of the force applied at an angle \(\theta\) from the vertical. The point A is on the wall and d signifies the vertical distance from A to B. ### Computation To determine the angular acceleration \(\vec{\alpha}\): \[ \alpha = \boxed{ \frac{}{} \, \hat{k} \, \text{rad} \, \text{s}^{-2} } \] ### Additional Note Hint: Watch your vector direction for \(\vec{\alpha}\) above. --- This problem is a practical application involving the concepts of torque, rotational motion, and the coefficient of friction. Use these fundamentals to solve for the angular acceleration of the toilet paper roll.
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