## Physics Problem: Toilet Paper Roll Angular Acceleration### ScenarioYou 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 ExplanationThe 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.### ComputationTo determine the angular acceleration \(\vec{\alpha}\):\[ \alpha = \boxed{ \frac{}{} \, \hat{k} \, \text{rad} \, \text{s}^{-2} } \]### Additional NoteHint: 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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TO || rad k

Elements Of Electromagnetics

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ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Question

## 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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