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• At the instant shown, the backhoe is traveling forward at a constant speed 𝑣0 and the boom ABC is rotating about the z axis with known angular velocity and angular acceleration 𝜔1, 𝛼1. At this same instant, the boom is rotating known angular velocity and angular acceleration 𝜔2, 𝛼2 relative to the frame.
• Determine the velocity and acceleration of point P at this instant

  1. Define position of A

  2. Calculate velocity of A

  3. Calculate acceleration of A

  4. Calculate total angular velocity of the boom

  5. Calculate angular acceleration of the boom

  6. Calculate position of P with respect to A

  7. Calculate velocity of P

  8. Calculate acceleration of P
• 𝒗𝐴


  𝒗𝑂 + 𝝎1 × 𝒓𝐴 + 𝒗𝐴/𝑂
• 𝒂𝐴


  𝒂𝑂 + 𝜶1 × 𝒓𝐴 + 𝝎𝟏 × 𝝎1 × 𝒓𝐴 + 2𝝎1 × 𝒗𝐴/𝑂 + 𝒂𝐴/𝑂
• 𝜴𝐴𝐵𝐶


  𝝎1 + ��2
• 𝜶𝐴𝐵𝐶


  𝑑𝝎1/𝑑�� + 𝑑𝝎2/𝑑𝑡
• 𝒓��𝑃


  6𝐿 Ƹ𝒊 + 2𝐿෡𝒌
• 𝒗𝑃


  𝒗𝐴 + 𝜴𝐴𝐵𝐶 × 𝒓𝐴𝑃 + 𝒗𝑃/𝐴
• 𝒂��


  𝒂𝐴 + 𝜶𝐴𝐵𝐶 × 𝒓𝐴𝑃 + 𝛀𝐴𝐵𝐶 × 𝛀𝐴𝐵𝐶 × 𝒓𝐴𝑃 + 2𝛀𝐴𝐵𝐶 × 𝒗𝑃/𝑨 + 𝒂𝑃/𝐴