The bar shown rotates about a fixed axis through point 0. At the instant shown, the bar has angular velocity w [rad/sec) and angular acceleration a [rad/sec"). Determine: 1. The velocity va [m/sec] of point A 2. The acceleration ag [m/sec²] of point A DA

Structural Analysis
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Chapter2: Loads On Structures
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The bar shown rotates about a fixed axis through point \(O\). At the instant shown, the bar has angular velocity \(\omega\) [rad/sec] and angular acceleration \(\alpha\) [rad/sec\(^2\)]. Determine:

1. The velocity \(v_A\) [m/sec] of point A
2. The acceleration \(a_A\) [m/sec\(^2\)] of point A

**Diagram Explanation:**

The diagram illustrates a bar of length \(L\) that rotates counterclockwise about a fixed point \(O\). The bar is inclined at an angle \(\theta\) from the vertical. The rotation axis is fixed, and the bar is shown at the position where it makes this angle \(\theta\). The following elements are depicted in the diagram:

- **Point \(O\)**: The fixed point about which the bar rotates.
- **Point \(A\)**: The end of the bar, a distance \(L\) from point \(O\).
- **Angular Velocity (\(\omega\))**: Shown as a green circular arrow indicating the rate of rotation.
- **Angular Acceleration (\(\alpha\))**: Shown as another notation beside \(\omega\).
- **Length \(L\)**: The total length of the bar from \(O\) to \(A\).
- **Angle \(\theta\)**: The angle between the bar and the vertical direction, marked on the bar.

The rotational motion involves both angular velocity (\(\omega\)) and angular acceleration (\(\alpha\)), which affect the linear velocity and linear acceleration of point \(A\).
Transcribed Image Text:The bar shown rotates about a fixed axis through point \(O\). At the instant shown, the bar has angular velocity \(\omega\) [rad/sec] and angular acceleration \(\alpha\) [rad/sec\(^2\)]. Determine: 1. The velocity \(v_A\) [m/sec] of point A 2. The acceleration \(a_A\) [m/sec\(^2\)] of point A **Diagram Explanation:** The diagram illustrates a bar of length \(L\) that rotates counterclockwise about a fixed point \(O\). The bar is inclined at an angle \(\theta\) from the vertical. The rotation axis is fixed, and the bar is shown at the position where it makes this angle \(\theta\). The following elements are depicted in the diagram: - **Point \(O\)**: The fixed point about which the bar rotates. - **Point \(A\)**: The end of the bar, a distance \(L\) from point \(O\). - **Angular Velocity (\(\omega\))**: Shown as a green circular arrow indicating the rate of rotation. - **Angular Acceleration (\(\alpha\))**: Shown as another notation beside \(\omega\). - **Length \(L\)**: The total length of the bar from \(O\) to \(A\). - **Angle \(\theta\)**: The angle between the bar and the vertical direction, marked on the bar. The rotational motion involves both angular velocity (\(\omega\)) and angular acceleration (\(\alpha\)), which affect the linear velocity and linear acceleration of point \(A\).
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