For the mechanism below, at this instant, angle = 41 rod BC has angular velocity W = 4.0 rad/s, and angular acceleration a = 2.0 rad/s². Link AC is pin-connected to collar C which slides freely on rod BC. Determine the magnitude of the angular acceleration in rad/s² of link AC at this instant. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point.

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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For the mechanism below, at this instant, angle \( \theta = 41^\circ \), rod \( BC \) has angular velocity \( \omega = 4.0 \, \text{rad/s} \), and angular acceleration \( \alpha = 2.0 \, \text{rad/s}^2 \). Link \( AC \) is pin-connected to collar \( C \) which slides freely on rod \( BC \). Determine the magnitude of the angular acceleration in \( \text{rad/s}^2 \) of link \( AC \) at this instant. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point.

**Diagram Explanation:**

The diagram shows a mechanism consisting of rods and a collar:

- Rod \( BC \) is inclined and pin-connected at point \( B \) on the horizontal ground.
- Collar \( C \) can slide freely along rod \( BC \).
- Link \( AC \) connects point \( A \), fixed on the ground 1 meter from \( B \), to collar \( C \).
- Angular velocity \( \omega \) is shown as a red arrow, and angular acceleration \( \alpha \) is shown as a green arrow, both acting along rod \( BC \).
- The angle \( \theta = 41^\circ \) is the inclination of rod \( BC \).

**Your Answer:**

\[ \text{Your Answer:} \] \_\_\_\_\_\_\_\_\_\_

\[ \text{Answer} \]
Transcribed Image Text:For the mechanism below, at this instant, angle \( \theta = 41^\circ \), rod \( BC \) has angular velocity \( \omega = 4.0 \, \text{rad/s} \), and angular acceleration \( \alpha = 2.0 \, \text{rad/s}^2 \). Link \( AC \) is pin-connected to collar \( C \) which slides freely on rod \( BC \). Determine the magnitude of the angular acceleration in \( \text{rad/s}^2 \) of link \( AC \) at this instant. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. **Diagram Explanation:** The diagram shows a mechanism consisting of rods and a collar: - Rod \( BC \) is inclined and pin-connected at point \( B \) on the horizontal ground. - Collar \( C \) can slide freely along rod \( BC \). - Link \( AC \) connects point \( A \), fixed on the ground 1 meter from \( B \), to collar \( C \). - Angular velocity \( \omega \) is shown as a red arrow, and angular acceleration \( \alpha \) is shown as a green arrow, both acting along rod \( BC \). - The angle \( \theta = 41^\circ \) is the inclination of rod \( BC \). **Your Answer:** \[ \text{Your Answer:} \] \_\_\_\_\_\_\_\_\_\_ \[ \text{Answer} \]
For the mechanism below, at this instant, angle \( \theta = 42^\circ \), rod \( BC \) has angular velocity \( \omega = 4.3 \, \text{rad/s} \), and angular acceleration \( \alpha = 3.0 \, \text{rad/s}^2 \). Link \( AC \) is pin-connected to collar \( C \) which slides freely on rod \( BC \). Determine the magnitude of the angular velocity of link \( AC \) at this instant. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point and proper unit.

**Diagram Explanation:**

The diagram shows a mechanical system consisting of a rod \( BC \) inclined at angle \( \theta \). The rod is connected at point \( B \) on a horizontal surface and has a collar \( C \) that slides freely along it. The setup includes:

- \( A \) and \( B \), which are two fixed points on the horizontal surface.
- The distance between points \( A \) and \( B \) is fixed at \( 1 \, \text{m} \).
- The angular velocity \( \omega \) is directed along the rod \( BC \).
- The angular acceleration \( \alpha \) is also directed along the rod \( BC \).

The goal is to calculate the angular velocity of link \( AC \), taking into account the given angular velocity and acceleration of rod \( BC \).

**Your Answer:**

\[
\begin{array}{cc}
\text{Answer} & \text{units} \\
\end{array}
\]
Transcribed Image Text:For the mechanism below, at this instant, angle \( \theta = 42^\circ \), rod \( BC \) has angular velocity \( \omega = 4.3 \, \text{rad/s} \), and angular acceleration \( \alpha = 3.0 \, \text{rad/s}^2 \). Link \( AC \) is pin-connected to collar \( C \) which slides freely on rod \( BC \). Determine the magnitude of the angular velocity of link \( AC \) at this instant. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point and proper unit. **Diagram Explanation:** The diagram shows a mechanical system consisting of a rod \( BC \) inclined at angle \( \theta \). The rod is connected at point \( B \) on a horizontal surface and has a collar \( C \) that slides freely along it. The setup includes: - \( A \) and \( B \), which are two fixed points on the horizontal surface. - The distance between points \( A \) and \( B \) is fixed at \( 1 \, \text{m} \). - The angular velocity \( \omega \) is directed along the rod \( BC \). - The angular acceleration \( \alpha \) is also directed along the rod \( BC \). The goal is to calculate the angular velocity of link \( AC \), taking into account the given angular velocity and acceleration of rod \( BC \). **Your Answer:** \[ \begin{array}{cc} \text{Answer} & \text{units} \\ \end{array} \]
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