The blades of a ceiling fan have a radius of 0.77 m and are rotating about a fixed axis with an angular velocity of -1.85 rad/s. When the switch is turned to a higher speed, the blades acquire an angular acceleration of -3.76 rad/s. After 5.68 s has elapsed since the switch was reset, what is (a) The total acceleration (in m/s?) of a point "A" on the tip of a blade and (b) The angle ø between the total acceleration a' and the centripetal acceleration a c? A Sketch the vectors at point A

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### Physics Problem: Ceiling Fan Blade Rotation

The blades of a ceiling fan have a radius of 0.77 m and are rotating about a fixed axis with an angular velocity of -1.85 rad/s. When the switch is turned to a higher speed, the blades acquire an angular acceleration of -3.76 rad/s². After 5.68 s has elapsed since the switch was reset, what is:
(a) The total acceleration (in m/s²) of a point “A” on the tip of a blade, and
(b) The angle θ between the total acceleration  **a** → and the centripetal acceleration **a** → c?

#### Explanation of Diagram:

The diagram below depicts a circle representing the rotating blade of a ceiling fan. A point "A" is marked on the circumference of the circle indicating the tip of the blade. The circle represents the path traced by point "A" due to the fan's rotation. 

![Diagram of rotating ceiling fan blade with point A at the tip](example_image.png)

For solving the problem:
1. **Find the total acceleration**: This involves calculating the tangential and centripetal accelerations at point A and combining them to get the magnitude of the total acceleration. 
2. **Determine the angle θ**: This angle is between the total acceleration vector and the centripetal acceleration vector.

#### Diagram Annotation:

Within the circle:
- The point at the edge labeled "A" represents the tip of the fan blade.
- An arrow representing the vector of the centripetal acceleration is directed towards the center of the circle.
- The tangential acceleration vector is tangent to the circle at point "A", directed either in the clockwise or counterclockwise direction depending on the direction of angular acceleration. 

Please provide any further calculations or representational vectors as required for a detailed solution.
Transcribed Image Text:### Physics Problem: Ceiling Fan Blade Rotation The blades of a ceiling fan have a radius of 0.77 m and are rotating about a fixed axis with an angular velocity of -1.85 rad/s. When the switch is turned to a higher speed, the blades acquire an angular acceleration of -3.76 rad/s². After 5.68 s has elapsed since the switch was reset, what is: (a) The total acceleration (in m/s²) of a point “A” on the tip of a blade, and (b) The angle θ between the total acceleration **a** → and the centripetal acceleration **a** → c? #### Explanation of Diagram: The diagram below depicts a circle representing the rotating blade of a ceiling fan. A point "A" is marked on the circumference of the circle indicating the tip of the blade. The circle represents the path traced by point "A" due to the fan's rotation. ![Diagram of rotating ceiling fan blade with point A at the tip](example_image.png) For solving the problem: 1. **Find the total acceleration**: This involves calculating the tangential and centripetal accelerations at point A and combining them to get the magnitude of the total acceleration. 2. **Determine the angle θ**: This angle is between the total acceleration vector and the centripetal acceleration vector. #### Diagram Annotation: Within the circle: - The point at the edge labeled "A" represents the tip of the fan blade. - An arrow representing the vector of the centripetal acceleration is directed towards the center of the circle. - The tangential acceleration vector is tangent to the circle at point "A", directed either in the clockwise or counterclockwise direction depending on the direction of angular acceleration. Please provide any further calculations or representational vectors as required for a detailed solution.
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