The moment of inertia for a rod rotating about its end is ML² The moment of inertia for a solid sphere rotating through its center is MR2 1. Caleulate the magnitude of the angular acceleration of this rod with mass 1kg, length Im. (X) 25 AXIS KF = 20N 2. Calculate the magnitude of the angular acceleration of this sphere with mass 1kg, radius Im. F = 8.5 N AXIS

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**Educational Content on Angular Acceleration**

**Introduction:**
Understanding the concept of angular acceleration is fundamental in the study of rotational dynamics. The moment of inertia is a critical factor in determining how an object accelerates when subjected to a force.

**Moments of Inertia:**
- For a rod rotating about its end, the moment of inertia is given by \(\frac{1}{3}ML^2\).
- For a solid sphere rotating through its center, the moment of inertia is \(\frac{2}{5}MR^2\).

**Problem Statements:**

**1. Rod Rotation:**

*A diagram accompanies this problem, showing a rod fixed at one end and free to rotate about an axis. A force \( F = 20 \, \text{N} \) is applied at the free end at an angle of \( 25^\circ \) to the rod.*

- **Objective:** Calculate the magnitude of the angular acceleration of this rod.
- **Given:**
  - Mass of the rod, \( M = 1 \, \text{kg} \)
  - Length of the rod, \( L = 1 \, \text{m} \)
  - Applied force, \( F = 20 \, \text{N} \)
  - Angle of force application, \( \theta = 25^\circ \)

**2. Sphere Rotation:**

*A diagram is provided showing a sphere with an axis through its center. A force \( F = 8.5 \, \text{N} \) is acting tangentially on the surface.*

- **Objective:** Calculate the magnitude of the angular acceleration of this sphere.
- **Given:**
  - Mass of the sphere, \( M = 1 \, \text{kg} \)
  - Radius of the sphere, \( R = 1 \, \text{m} \)
  - Applied force, \( F = 8.5 \, \text{N} \)

**Diagrams:**

**1. Rod:** The rod is horizontal with one end marked as the axis. The angle of \( 25^\circ \) is between the rod and the direction of the applied force. This setup is crucial for calculating the torque, which is influenced by the angle of force application.

**2. Sphere:** The sphere is shown with a central axis, and the force \( F = 8.5 \
Transcribed Image Text:**Educational Content on Angular Acceleration** **Introduction:** Understanding the concept of angular acceleration is fundamental in the study of rotational dynamics. The moment of inertia is a critical factor in determining how an object accelerates when subjected to a force. **Moments of Inertia:** - For a rod rotating about its end, the moment of inertia is given by \(\frac{1}{3}ML^2\). - For a solid sphere rotating through its center, the moment of inertia is \(\frac{2}{5}MR^2\). **Problem Statements:** **1. Rod Rotation:** *A diagram accompanies this problem, showing a rod fixed at one end and free to rotate about an axis. A force \( F = 20 \, \text{N} \) is applied at the free end at an angle of \( 25^\circ \) to the rod.* - **Objective:** Calculate the magnitude of the angular acceleration of this rod. - **Given:** - Mass of the rod, \( M = 1 \, \text{kg} \) - Length of the rod, \( L = 1 \, \text{m} \) - Applied force, \( F = 20 \, \text{N} \) - Angle of force application, \( \theta = 25^\circ \) **2. Sphere Rotation:** *A diagram is provided showing a sphere with an axis through its center. A force \( F = 8.5 \, \text{N} \) is acting tangentially on the surface.* - **Objective:** Calculate the magnitude of the angular acceleration of this sphere. - **Given:** - Mass of the sphere, \( M = 1 \, \text{kg} \) - Radius of the sphere, \( R = 1 \, \text{m} \) - Applied force, \( F = 8.5 \, \text{N} \) **Diagrams:** **1. Rod:** The rod is horizontal with one end marked as the axis. The angle of \( 25^\circ \) is between the rod and the direction of the applied force. This setup is crucial for calculating the torque, which is influenced by the angle of force application. **2. Sphere:** The sphere is shown with a central axis, and the force \( F = 8.5 \
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