Multiple-Concept Example 7 explores the approach taken in problems such as this one. The blades of a ceiling fan have a radius of 0.331 m and are rotating about a fixed axis with an angular velocity of +1.22 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of +2.12 rad/s². After 0.326 s have elapsed since the switch was reset, what is (a) the total acceleration (in m/s2) of a point on the tip of a blade and (b) the angle between the total acceleration a and the centripetal acceleration a, (See Figure b)? (b) ar

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Multiple-Concept Example 7:**

This example explores the approach taken in problems such as the following. The blades of a ceiling fan have a radius of 0.331 meters and are rotating about a fixed axis with an angular velocity of +1.22 radians per second. When the fan is switched to a higher speed, the blades acquire an angular acceleration of +2.12 radians per second squared. 

**Problem:**
After 0.326 seconds have elapsed since the switch was reset, determine:
- (a) The total acceleration (in meters per second squared) of a point on the tip of a blade.
- (b) The angle θ between the total acceleration **a** and the centripetal acceleration **a<sub>c</sub>**.

**Diagram Description:**

1. **Diagram (a):** Shows a top view of the fan's rotating blades, with a point marked on the tip of one blade. The diagram illustrates the direction of angular velocity and angular acceleration.

2. **Diagram (b):** Depicts a vector representation of the total acceleration **a** and its two components: tangential acceleration **a<sub>t</sub>** and centripetal acceleration **a<sub>c</sub>**. The angle θ between **a** and **a<sub>c</sub>** is highlighted.

**Answer Fields:**

- (a) Number [Input Field] Units [Dropdown]
- (b) Number [Input Field] Units [Dropdown]
Transcribed Image Text:**Multiple-Concept Example 7:** This example explores the approach taken in problems such as the following. The blades of a ceiling fan have a radius of 0.331 meters and are rotating about a fixed axis with an angular velocity of +1.22 radians per second. When the fan is switched to a higher speed, the blades acquire an angular acceleration of +2.12 radians per second squared. **Problem:** After 0.326 seconds have elapsed since the switch was reset, determine: - (a) The total acceleration (in meters per second squared) of a point on the tip of a blade. - (b) The angle θ between the total acceleration **a** and the centripetal acceleration **a<sub>c</sub>**. **Diagram Description:** 1. **Diagram (a):** Shows a top view of the fan's rotating blades, with a point marked on the tip of one blade. The diagram illustrates the direction of angular velocity and angular acceleration. 2. **Diagram (b):** Depicts a vector representation of the total acceleration **a** and its two components: tangential acceleration **a<sub>t</sub>** and centripetal acceleration **a<sub>c</sub>**. The angle θ between **a** and **a<sub>c</sub>** is highlighted. **Answer Fields:** - (a) Number [Input Field] Units [Dropdown] - (b) Number [Input Field] Units [Dropdown]
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