2. The figure at the right shows a uniform disk that can rotate around a fixed axis through its center. (The axis is perpendic- ular to the page.) The disk has a radius of 0.02 m and a mass of 0.02 kg, and is initially at rest. Starting at time t = 0, two forces are applied tangentially to the rim as indicated. The force F₁ has a magnitude of 0.1 N, and the force F₂ has a magnitude of 0.15 N. TE ☐ k KO (.m Î

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**Problem Statement:**

2. The figure shows a uniform disk that can rotate around a fixed axis through its center, perpendicular to the page. The disk has a radius of 0.02 m and a mass of 0.02 kg, and is initially at rest. At time \( t = 0 \), two forces are applied tangentially to the rim as indicated. The force \( \vec{F}_1 \) has a magnitude of 0.1 N, and the force \( \vec{F}_2 \) has a magnitude of 0.15 N.

**Diagram Explanation:**

The diagram illustrates a top view of the disk with vectors representing the forces. The disk's center is marked with a small black dot. \( \vec{F}_1 \) is directed horizontally to the right and tangential to the disk at an angle, while \( \vec{F}_2 \) is directed downward and tangential to the rim. The coordinate axes \( \hat{i} \), \( \hat{j} \), and \( \hat{k} \) are shown next to the disk.

**Questions:**

(a) Indicate the directions (\( \pm \hat{k} \)) of the following:

- \( \vec{\tau}_1 \), the torque due to \( \vec{F}_1 \)
- \( \vec{\tau}_2 \), the torque due to \( \vec{F}_2 \)
- \( \vec{\alpha} \), the angular acceleration after the disk starts rotating.
- \( \vec{\omega} \), the angular velocity after the disk starts rotating.

(b) What is the angular momentum \( \vec{L} \) of the disk after the forces at \( t = 10 \, \text{s} \)?

*Note: The moment of inertia for a uniform disk is \( I = \frac{1}{2} MR^2 \).*
Transcribed Image Text:**Problem Statement:** 2. The figure shows a uniform disk that can rotate around a fixed axis through its center, perpendicular to the page. The disk has a radius of 0.02 m and a mass of 0.02 kg, and is initially at rest. At time \( t = 0 \), two forces are applied tangentially to the rim as indicated. The force \( \vec{F}_1 \) has a magnitude of 0.1 N, and the force \( \vec{F}_2 \) has a magnitude of 0.15 N. **Diagram Explanation:** The diagram illustrates a top view of the disk with vectors representing the forces. The disk's center is marked with a small black dot. \( \vec{F}_1 \) is directed horizontally to the right and tangential to the disk at an angle, while \( \vec{F}_2 \) is directed downward and tangential to the rim. The coordinate axes \( \hat{i} \), \( \hat{j} \), and \( \hat{k} \) are shown next to the disk. **Questions:** (a) Indicate the directions (\( \pm \hat{k} \)) of the following: - \( \vec{\tau}_1 \), the torque due to \( \vec{F}_1 \) - \( \vec{\tau}_2 \), the torque due to \( \vec{F}_2 \) - \( \vec{\alpha} \), the angular acceleration after the disk starts rotating. - \( \vec{\omega} \), the angular velocity after the disk starts rotating. (b) What is the angular momentum \( \vec{L} \) of the disk after the forces at \( t = 10 \, \text{s} \)? *Note: The moment of inertia for a uniform disk is \( I = \frac{1}{2} MR^2 \).*
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