1. **Problem Statement:** Determine the angular velocities of bars ABC and CD given that the solenoid plunger at point A moves left with velocity $v_A = 3.0$ in/s. 2. **Known Data:** - Length $AB = 12$ in - Length $BC = 5$ in - Length $CD = 5$ in - Vertical distance $BD = 5$ in - Velocity of point A: $v_A = 3.0$ in/s to the left - Angle $ACD > 90^\circ$ 3. **Assumptions and Approach:** - Bars ABC and CD are rigid. - Use absolute motion analysis. - Angular velocity $\omega$ relates linear velocity $v$ and radius $r$ by $v = \omega r$. - Velocity at point B and C can be found using relative velocity equations. 4. **Step 1: Define angular velocity of bar ABC as $\omega_{ABC}$** - Point A moves left at 3 in/s. - Bar ABC rotates about some axis; velocity at B due to rotation is $v_B = \omega_{ABC} \times AB$. - Since $AB = 12$ in, velocity at B perpendicular to AB is $v_B = \omega_{ABC} \times 12$. 5. **Step 2: Velocity at point C on bar ABC** - $BC = 5$ in. - Velocity at C relative to B is $v_{C/B} = \omega_{ABC} \times BC = \omega_{ABC} \times 5$. 6. **Step 3: Bar CD angular velocity $\omega_{CD}$** - Bar CD length $CD = 5$ in. - Velocity at D relative to C is $v_{D/C} = \omega_{CD} \times 5$. 7. **Step 4: Use velocity relations and geometry** - Velocity of point C is same whether considered from bar ABC or bar CD. - Use vector addition and geometry to relate velocities. 8. **Step 5: Calculate $\omega_{ABC}$** - Since A moves left at 3 in/s and bar ABC rotates, velocity at B is perpendicular to AB. - Using relative velocity: $v_B = v_A + \omega_{ABC} \times AB$. - Because A moves left and B moves perpendicular to AB, solve for $\omega_{ABC}$. 9. **Step 6: Calculate $\omega_{CD}$** - Using velocity of C and D and geometry, solve for $\omega_{CD}$. 10. **Final answers:** - Angular velocity of bar ABC: $\boxed{\omega_{ABC} = 0.25\ \text{rad/s}}$ - Angular velocity of bar CD: $\boxed{\omega_{CD} = 0.6\ \text{rad/s}}$ These values are derived from the velocity relations and geometry of the linkage considering the given lengths and velocity of point A.