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18-45. The 12-kg slender rod is attached to a spring, which has an unstretched length of 2 m. If the rod is released from rest when = 30°, determine its angular velocity at the instant = 90°. 2m

18-45. The 12-kg slender rod is attached to a spring, which has an unstretched length of 2 m. If the rod is released from rest when = 30°, determine its angular velocity at the instant = 90°. 2m

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Problem Statement:** The 12-kg slender rod is attached to a spring, which has an unstretched length of 2 meters. If the rod is released from rest when \( \theta = 30° \), determine its angular velocity at the instant \( \theta = 90° \). **Diagram Explanation:** The diagram visualizes a physics problem involving a slender rod and a spring. Here is a detailed explanation of the diagram: 1. **Rod Setup**: - A slender rod, identified at points A, B, and C, is shown. - Point A represents the pivot point where the rod is attached to a fixed support. - Points B and A have a horizontal distance of 2 meters. - Points A and C have a vertical distance of 2 meters, with point C indicating the free end of the rod. 2. **Spring Connection**: - A spring is attached to the setup, with a spring constant of \( k = 40 \, \text{N/m} \). - The unstretched length of the spring is 2 meters. - The spring is connected from point B (on the fixed support) to point C (the free end of the rod). 3. **Rod Position and Angle**: - The initial position of the rod is inclined at an angle \( \theta = 30° \) relative to the horizontal axis. - The task is to determine the rod's angular velocity at the instant when the angle \( \theta = 90° \) (when the rod is vertical). **Objective**: - Calculate the angular velocity of the rod at the instant \( \theta = 90° \). This educational content assists students in understanding the relationship between angular motion, spring dynamics, and rigid body mechanics.
Transcribed Image Text:**Problem Statement:** The 12-kg slender rod is attached to a spring, which has an unstretched length of 2 meters. If the rod is released from rest when \( \theta = 30° \), determine its angular velocity at the instant \( \theta = 90° \). **Diagram Explanation:** The diagram visualizes a physics problem involving a slender rod and a spring. Here is a detailed explanation of the diagram: 1. **Rod Setup**: - A slender rod, identified at points A, B, and C, is shown. - Point A represents the pivot point where the rod is attached to a fixed support. - Points B and A have a horizontal distance of 2 meters. - Points A and C have a vertical distance of 2 meters, with point C indicating the free end of the rod. 2. **Spring Connection**: - A spring is attached to the setup, with a spring constant of \( k = 40 \, \text{N/m} \). - The unstretched length of the spring is 2 meters. - The spring is connected from point B (on the fixed support) to point C (the free end of the rod). 3. **Rod Position and Angle**: - The initial position of the rod is inclined at an angle \( \theta = 30° \) relative to the horizontal axis. - The task is to determine the rod's angular velocity at the instant when the angle \( \theta = 90° \) (when the rod is vertical). **Objective**: - Calculate the angular velocity of the rod at the instant \( \theta = 90° \). This educational content assists students in understanding the relationship between angular motion, spring dynamics, and rigid body mechanics.
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