The 6.0-1b bar is pinned at its center O and connected to a torsional spring. The spring has a stiffness 5.4 lb ft/rad, so that the torque developed is M = (5.40) lb ft, where is in radians. (Figure 1) Part A If the bar is released from rest when it is vertical at = 90°, determine its angular velocity at the instant 0=0°. Express your answer to three significant figures and include the appropriate units.

The 6.0-1b bar is pinned at its center O and connected to a torsional spring. The spring has a stiffness 5.4 lb ft/rad, so that the torque developed is M = (5.40) lb ft, where is in radians. (Figure 1) Part A If the bar is released from rest when it is vertical at = 90°, determine its angular velocity at the instant 0=0°. Express your answer to three significant figures and include the appropriate units.

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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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

The image shows a mechanical dynamics problem involving a 6.0-lb bar that is pinned at its center point \( O \) and connected to a torsional spring. The spring has a stiffness of 5.4 lb·ft/rad, which causes the torque developed on the bar to be \( M = (5.4\theta) \) lb·ft, where \( \theta \) is the angle in radians.

**Figure Explanation:**
The figure illustrates the bar setup:
- A horizontal bar, 2 feet in total length, with each side extending 1 foot from the center point \( O \).
- The bar is shown with angle indicators suggesting it can rotate about the center \( O \), connected to a spring mechanism.

**Problem Statement:**
- **Part A:** If the bar is released from rest when it is vertical at \( \theta = 90^\circ \), the task is to determine its angular velocity at the instant \( \theta = 0^\circ \).
- It is required to express the answer to three significant figures and include the appropriate units.

**Answer Input Section:**
- A submission box is provided to enter the angular velocity \( \omega \) with fields for both value and units.

**User Actions Available:**
- Submit the answer.
- Request the answer.
- Provide feedback on the task.

This problem involves concepts of rotational motion, including torque and angular velocity, and requires applying the principles of dynamics and energy conservation.

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