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3. The bar shown rotates about the z-axis. Find the velocity and accleration of point P for the instant when the angular aceleration is 4 rad/s² and angular velocity is 1.5 rad/s, both in the directions shown. Give your answers in terms of the given Cartesian coordinates. Note: This problem is trying to fool you. The position vector re must be normal to the axis of rotation, which is not from point O. a 500 mm, P 50 mm 200 mm

3. The bar shown rotates about the z-axis. Find the velocity and accleration of point P for the instant when the angular aceleration is 4 rad/s² and angular velocity is 1.5 rad/s, both in the directions shown. Give your answers in terms of the given Cartesian coordinates. Note: This problem is trying to fool you. The position vector re must be normal to the axis of rotation, which is not from point O. a 500 mm, P 50 mm 200 mm

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:** 3. The bar shown rotates about the z-axis. Find the velocity and acceleration of point \( P \) for the instant when the angular acceleration is \( 4 \, \text{rad/s}^2 \) and angular velocity is \( 1.5 \, \text{rad/s} \), both in the directions shown. Give your answers in terms of the given Cartesian coordinates. **Note:** This problem is trying to fool you. The position vector \( \mathbf{r}_P \) must be normal to the axis of rotation, which is not from point \( O \). **Diagram Description:** The diagram is in a 3D Cartesian coordinate system with axes labeled \( x \), \( y \), and \( z \). A bar is shown extending from the point of rotation. - The primary axis of rotation is the \( z \)-axis. - The bar is 500 mm in length from the axis of rotation to point \( P \). - Point \( P \) is located at the end of a secondary segment 200 mm from a joint perpendicular to the main bar. - Angular velocity (\( \omega \)) is shown around the \( z \)-axis, indicating rotation. - A position vector \( \mathbf{r}_P \) extends from the axis of rotation to point \( P \). The challenge in the problem is to calculate the required velocity and acceleration, ensuring that the position vector \( \mathbf{r}_P \) is correctly oriented normal to the axis of rotation.
Transcribed Image Text:**Problem Statement:** 3. The bar shown rotates about the z-axis. Find the velocity and acceleration of point \( P \) for the instant when the angular acceleration is \( 4 \, \text{rad/s}^2 \) and angular velocity is \( 1.5 \, \text{rad/s} \), both in the directions shown. Give your answers in terms of the given Cartesian coordinates. **Note:** This problem is trying to fool you. The position vector \( \mathbf{r}_P \) must be normal to the axis of rotation, which is not from point \( O \). **Diagram Description:** The diagram is in a 3D Cartesian coordinate system with axes labeled \( x \), \( y \), and \( z \). A bar is shown extending from the point of rotation. - The primary axis of rotation is the \( z \)-axis. - The bar is 500 mm in length from the axis of rotation to point \( P \). - Point \( P \) is located at the end of a secondary segment 200 mm from a joint perpendicular to the main bar. - Angular velocity (\( \omega \)) is shown around the \( z \)-axis, indicating rotation. - A position vector \( \mathbf{r}_P \) extends from the axis of rotation to point \( P \). The challenge in the problem is to calculate the required velocity and acceleration, ensuring that the position vector \( \mathbf{r}_P \) is correctly oriented normal to the axis of rotation.
Expert Solution
Step 1

Given:

Angular acceleration of the bar:

→α=4 rad/s2       (clockwise)

Angular velocity of the bar:

→ω=1.5 rad/s        (counter clockwise)

From the given diagram:

The distance of point P from the axis of the rotation of the bar:

→rp=0.52+0.22         =0.53 m

And angle made by rp from x axis:

→θ=tan-1200500=21.80°

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