### Angular Motion Analysis#### Problem Statement:Member \( AB \) exhibits specific angular motions. Your task is to determine the following:1. The velocity of slider \( C \).2. The angular velocity of member \( BC \).3. The acceleration of slider \( C \).4. The angular acceleration of member \( BC \).#### Given Data:- Angular velocity of \( AB \), \( \omega_{AB} = 2 \text{ rad/s} \).- Angular acceleration of \( AB \), \( \alpha_{AB} = 4 \text{ rad/s}^2 \).- Length of \( AB = 0.5 \text{ m} \).- Length of \( BC = 1.5 \text{ m} \).- Angle \( \theta = 45^\circ \).#### Diagram Explanation:The diagram illustrates member \( AB \) and \( BC \):1. Point \( A \) is the point of rotation.2. Member \( AB \) rotates with an angular velocity \( \omega_{AB} \) and an angular acceleration \( \alpha_{AB} \).3. \( AB \) has a length of 0.5 meters and rotates at a \( 45^\circ \) angle from the horizontal.4. Member \( BC \) connects point \( B \) to the slider \( C \). \( BC \) has a length of 1.5 meters and is horizontal to the slider \( C \).#### Required Calculations:1. **Velocity of Slider \( C \)**: - Use the relationship between linear velocity and angular velocity. - Velocity, \( v_B = \omega_{AB} \times AB \). - Decompose \( v_B \) into horizontal and vertical components. - Develop the relative velocity equation for \( C \) considering the horizontal motion.2. **Angular Velocity of Member \( BC \)**: - Determine components of velocity at \( B \) and relate them to point \( C \).3. **Acceleration of Slider \( C \)**: - Similar to velocity determination, use angular acceleration \( \alpha_{AB} \) to find linear acceleration. - Calculate tangential and radial components of acceleration at \( B \).4. **Angular Acceleration of Member \( BC \)**: - Use kinematic relationships between the motion of points \( B \) and \( C \).###

Member AB has the angular motions shown. Determine the velocity of slider C, the angular velocity of member BC, the acceleration of slider C, and the angular acceleration of member BC. WA AB = 2 rad/s = 4 rad/s² 0.5 m A B 0 = 45° 1.5 m

Member AB has the angular motions shown. Determine the velocity of slider C, the angular velocity of member BC, the acceleration of slider C, and the angular acceleration of member BC. WA AB = 2 rad/s = 4 rad/s² 0.5 m A B 0 = 45° 1.5 m

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Question

### Angular Motion Analysis

#### Problem Statement:
Member \( AB \) exhibits specific angular motions. Your task is to determine the following:
1. The velocity of slider \( C \).
2. The angular velocity of member \( BC \).
3. The acceleration of slider \( C \).
4. The angular acceleration of member \( BC \).

#### Given Data:
- Angular velocity of \( AB \), \( \omega_{AB} = 2 \text{ rad/s} \).
- Angular acceleration of \( AB \), \( \alpha_{AB} = 4 \text{ rad/s}^2 \).
- Length of \( AB = 0.5 \text{ m} \).
- Length of \( BC = 1.5 \text{ m} \).
- Angle \( \theta = 45^\circ \).

#### Diagram Explanation:
The diagram illustrates member \( AB \) and \( BC \):
1. Point \( A \) is the point of rotation.
2. Member \( AB \) rotates with an angular velocity \( \omega_{AB} \) and an angular acceleration \( \alpha_{AB} \).
3. \( AB \) has a length of 0.5 meters and rotates at a \( 45^\circ \) angle from the horizontal.
4. Member \( BC \) connects point \( B \) to the slider \( C \). \( BC \) has a length of 1.5 meters and is horizontal to the slider \( C \).

#### Required Calculations:
1. **Velocity of Slider \( C \)**:
- Use the relationship between linear velocity and angular velocity.
- Velocity, \( v_B = \omega_{AB} \times AB \).
- Decompose \( v_B \) into horizontal and vertical components.
- Develop the relative velocity equation for \( C \) considering the horizontal motion.

2. **Angular Velocity of Member \( BC \)**:
- Determine components of velocity at \( B \) and relate them to point \( C \).

3. **Acceleration of Slider \( C \)**:
- Similar to velocity determination, use angular acceleration \( \alpha_{AB} \) to find linear acceleration.
- Calculate tangential and radial components of acceleration at \( B \).

4. **Angular Acceleration of Member \( BC \)**:
- Use kinematic relationships between the motion of points \( B \) and \( C \).

###

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