Calculate the acceleration of point A with respect to origin point 0. Remember that like velocity, you need to calculate each link's relative velocity and then add them all up: aA/O = a4/3 + aB/0 Also, each relative acceleration can be calculated using its two components in radial and direction, for example: a4/B = ar, A/B + ag, A/B 0, 0̟, ö ri = 25.0cm 01 = 45.0deg wi = 0.5rad/s a1 = 1.0rad/s² r2 0 = 45deg r2 = 20.0cm 82 = 30.0deg 02 = 30.0deg w2 = 0.5rad/s a2 = 0.0rad/s²
Calculate the acceleration of point A with respect to origin point 0. Remember that like velocity, you need to calculate each link's relative velocity and then add them all up: aA/O = a4/3 + aB/0 Also, each relative acceleration can be calculated using its two components in radial and direction, for example: a4/B = ar, A/B + ag, A/B 0, 0̟, ö ri = 25.0cm 01 = 45.0deg wi = 0.5rad/s a1 = 1.0rad/s² r2 0 = 45deg r2 = 20.0cm 82 = 30.0deg 02 = 30.0deg w2 = 0.5rad/s a2 = 0.0rad/s²
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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![# Calculating the Acceleration of Point A
To find the acceleration of point A relative to the origin point O, follow this approach:
### Key Steps:
1. **Calculate Relative Velocity**:
- The velocity of point A relative to point O (\(\vec{a}_{A/O}\)) is determined by summing the relative velocities of each link.
2. **Use the Formula**:
\[
\vec{a}_{A/O} = \vec{a}_{A/B} + \vec{a}_{B/O}
\]
3. **Compute Each Component of Acceleration**:
- Each relative acceleration can be broken down into radial and tangential components. For instance:
\[
\vec{a}_{A/B} = a_{r, A/B} + a_{\theta, A/B}
\]
### Diagram Explanation:
- The diagram shows a mechanical linkage system with two links, \(O\) to \(A\) and \(O\) to \(B\).
- **Link Parameters**:
- **Link \(r_1\)** has a length of 25 cm and an angle \(\theta_1\) of 45 degrees.
- It rotates with an angular velocity of \(\omega_1 = 0.5 \, \text{rad/s}\) and an angular acceleration of \(\alpha_1 = 1.0 \, \text{rad/s}^2\).
- **Link \(r_2\)** is 20 cm long at an angle \(\theta_2\) of 30 degrees.
- This link has \(\omega_2 = 0.5 \, \text{rad/s}\) and \(\alpha_2 = 0 \, \text{rad/s}^2\).
- **Diagram Components**:
- The aligned links, circular arcs, and angular velocities/accelerations are shown with arrows to indicate direction. The points O, A, and B are labeled for reference.
By following these guidelines, you’ll effectively work through the vector calculations required to find the desired accelerations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b08af6d-b43b-40f9-8ead-23581b49f3e1%2F695d3b0b-e572-49f5-92d7-410413852fcb%2Feo21hif_processed.png&w=3840&q=75)
Transcribed Image Text:# Calculating the Acceleration of Point A
To find the acceleration of point A relative to the origin point O, follow this approach:
### Key Steps:
1. **Calculate Relative Velocity**:
- The velocity of point A relative to point O (\(\vec{a}_{A/O}\)) is determined by summing the relative velocities of each link.
2. **Use the Formula**:
\[
\vec{a}_{A/O} = \vec{a}_{A/B} + \vec{a}_{B/O}
\]
3. **Compute Each Component of Acceleration**:
- Each relative acceleration can be broken down into radial and tangential components. For instance:
\[
\vec{a}_{A/B} = a_{r, A/B} + a_{\theta, A/B}
\]
### Diagram Explanation:
- The diagram shows a mechanical linkage system with two links, \(O\) to \(A\) and \(O\) to \(B\).
- **Link Parameters**:
- **Link \(r_1\)** has a length of 25 cm and an angle \(\theta_1\) of 45 degrees.
- It rotates with an angular velocity of \(\omega_1 = 0.5 \, \text{rad/s}\) and an angular acceleration of \(\alpha_1 = 1.0 \, \text{rad/s}^2\).
- **Link \(r_2\)** is 20 cm long at an angle \(\theta_2\) of 30 degrees.
- This link has \(\omega_2 = 0.5 \, \text{rad/s}\) and \(\alpha_2 = 0 \, \text{rad/s}^2\).
- **Diagram Components**:
- The aligned links, circular arcs, and angular velocities/accelerations are shown with arrows to indicate direction. The points O, A, and B are labeled for reference.
By following these guidelines, you’ll effectively work through the vector calculations required to find the desired accelerations.
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