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The large blade of a helicopter is rotating in a horizontal circle. The length of the blade is 7.77 m, measured from its tip to the center of the circle. Find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point located 2.49 m from the center of the circle.

The large blade of a helicopter is rotating in a horizontal circle. The length of the blade is 7.77 m, measured from its tip to the center of the circle. Find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point located 2.49 m from the center of the circle.

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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The large blade of a helicopter is rotating in a horizontal circle. The length of the blade is 7.77 m, measured from its tip to the center of the circle. Find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point located 2.49 m from the center of the circle.

### Helicopter Rotor Dynamics This diagram illustrates the dynamics of a helicopter rotor, highlighting the motion and forces acting on the rotor blade. #### Key Components: 1. **Helicopter View:** - The diagram provides an aerial view of a helicopter with its main rotor visible. 2. **Rotor Blades:** - The rotor consists of several spinning blades. One blade is shown prominently, extending outward. 3. **Rotational Motion:** - The rotor spins about a central axis, creating circular paths represented by dotted circles. 4. **Distance from Axis:** - Two radii, \( r_1 \) and \( r_2 \), are marked from the center of rotation to two points on the blade, illustrating different radial distances. 5. **Centripetal Acceleration:** - Two vectors, \( a_{c1} \) and \( a_{c2} \), are depicted at different points on the rotor blade, showing the direction of centripetal acceleration. - \( a_{c1} \) is longer and located further from the center, indicating greater acceleration at a larger radius. - \( a_{c2} \) is shorter and closer to the center, indicating lesser acceleration at a smaller radius. #### Concepts Illustrated: - **Centripetal Acceleration (\( a_c \)):** - The acceleration directed towards the center of the circular path. It increases with distance from the axis due to higher linear velocity at larger radii. - **Rotational Dynamics:** - The diagram effectively demonstrates how different sections of the rotor blade experience varying levels of acceleration, crucial for understanding rotor blade stress and dynamics. This illustration aids in comprehending the fundamental principles of rotor blade mechanics and the varying forces experienced along the blade span.
Transcribed Image Text:### Helicopter Rotor Dynamics This diagram illustrates the dynamics of a helicopter rotor, highlighting the motion and forces acting on the rotor blade. #### Key Components: 1. **Helicopter View:** - The diagram provides an aerial view of a helicopter with its main rotor visible. 2. **Rotor Blades:** - The rotor consists of several spinning blades. One blade is shown prominently, extending outward. 3. **Rotational Motion:** - The rotor spins about a central axis, creating circular paths represented by dotted circles. 4. **Distance from Axis:** - Two radii, \( r_1 \) and \( r_2 \), are marked from the center of rotation to two points on the blade, illustrating different radial distances. 5. **Centripetal Acceleration:** - Two vectors, \( a_{c1} \) and \( a_{c2} \), are depicted at different points on the rotor blade, showing the direction of centripetal acceleration. - \( a_{c1} \) is longer and located further from the center, indicating greater acceleration at a larger radius. - \( a_{c2} \) is shorter and closer to the center, indicating lesser acceleration at a smaller radius. #### Concepts Illustrated: - **Centripetal Acceleration (\( a_c \)):** - The acceleration directed towards the center of the circular path. It increases with distance from the axis due to higher linear velocity at larger radii. - **Rotational Dynamics:** - The diagram effectively demonstrates how different sections of the rotor blade experience varying levels of acceleration, crucial for understanding rotor blade stress and dynamics. This illustration aids in comprehending the fundamental principles of rotor blade mechanics and the varying forces experienced along the blade span.
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