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Starting from rest, an airplane propeller begins to rotate with an angular acceleration a = 0.0600 rad/s². The propeller radius is 60.0 cm. After exactly 4.00 seconds, calculate the total linear acceleration of the tip of the propeller. (The total linear acceleration is the vector combination of the tangential acceleration and the centripetal acceleration.) r= 60.0 cm

Starting from rest, an airplane propeller begins to rotate with an angular acceleration a = 0.0600 rad/s². The propeller radius is 60.0 cm. After exactly 4.00 seconds, calculate the total linear acceleration of the tip of the propeller. (The total linear acceleration is the vector combination of the tangential acceleration and the centripetal acceleration.) r= 60.0 cm

College Physics
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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**Problem: Calculating Linear Acceleration of an Airplane Propeller Tip** Starting from rest, an airplane propeller begins to rotate with an angular acceleration \( \alpha = 0.0600 \, \text{rad/s}^2 \). The propeller radius is 60.0 cm. After exactly 4.00 seconds, calculate the total linear acceleration of the tip of the propeller. (The total linear acceleration is the vector combination of the tangential acceleration and the centripetal acceleration.) **Diagram Explanation:** A diagram shows an airplane propeller viewed from the side, rotating in a clockwise direction. The propeller has a radius of \( r = 60.0 \, \text{cm} \). The radius is shown with a line extending from the center to the tip of one of the propeller blades. **Calculations:** 1. **Angular Acceleration**: - \( \alpha = 0.0600 \, \text{rad/s}^2 \) 2. **Radius**: - \( r = 60.0 \, \text{cm} = 0.60 \, \text{m} \) 3. **Time**: - \( t = 4.00 \, \text{s} \) 4. **Angular Velocity**: - \( \omega = \alpha \times t = 0.0600 \, \text{rad/s}^2 \times 4.00 \, \text{s} = 0.240 \, \text{rad/s} \) 5. **Tangential Acceleration**: - \( a_t = \alpha \times r = 0.0600 \, \text{rad/s}^2 \times 0.60 \, \text{m} = 0.0360 \, \text{m/s}^2 \) 6. **Centripetal Acceleration**: - \( a_c = \omega^2 \times r = (0.240 \, \text{rad/s})^2 \times 0.60 \, \text{m} = 0.03456 \, \text{m/s}^2 \) 7. **Total Linear Acceleration**: - \( a = \sqrt{a_t^2 + a_c^2} = \sqrt{(0.
Transcribed Image Text:**Problem: Calculating Linear Acceleration of an Airplane Propeller Tip** Starting from rest, an airplane propeller begins to rotate with an angular acceleration \( \alpha = 0.0600 \, \text{rad/s}^2 \). The propeller radius is 60.0 cm. After exactly 4.00 seconds, calculate the total linear acceleration of the tip of the propeller. (The total linear acceleration is the vector combination of the tangential acceleration and the centripetal acceleration.) **Diagram Explanation:** A diagram shows an airplane propeller viewed from the side, rotating in a clockwise direction. The propeller has a radius of \( r = 60.0 \, \text{cm} \). The radius is shown with a line extending from the center to the tip of one of the propeller blades. **Calculations:** 1. **Angular Acceleration**: - \( \alpha = 0.0600 \, \text{rad/s}^2 \) 2. **Radius**: - \( r = 60.0 \, \text{cm} = 0.60 \, \text{m} \) 3. **Time**: - \( t = 4.00 \, \text{s} \) 4. **Angular Velocity**: - \( \omega = \alpha \times t = 0.0600 \, \text{rad/s}^2 \times 4.00 \, \text{s} = 0.240 \, \text{rad/s} \) 5. **Tangential Acceleration**: - \( a_t = \alpha \times r = 0.0600 \, \text{rad/s}^2 \times 0.60 \, \text{m} = 0.0360 \, \text{m/s}^2 \) 6. **Centripetal Acceleration**: - \( a_c = \omega^2 \times r = (0.240 \, \text{rad/s})^2 \times 0.60 \, \text{m} = 0.03456 \, \text{m/s}^2 \) 7. **Total Linear Acceleration**: - \( a = \sqrt{a_t^2 + a_c^2} = \sqrt{(0.
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