Pulley w/ 3 Masses Homework: Find Linear Acceleration

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SUMMARY

The problem involves calculating the linear acceleration of a system consisting of a green hoop (mass mh = 2.4 kg, radius Rh = 0.12 m), a blue solid disk pulley (mass md = 2.4 kg, radius Rd = 0.11 m), and an orange sphere (mass ms = 4.2 kg, radius Rs = 0.25 m) that rolls without slipping. The system is released from rest, and the challenge is to account for the mass of the pulley in the calculations. The solution requires applying Newton's second law and rotational dynamics principles to derive the linear acceleration of the hoop.

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  • Understanding of Newton's second law of motion
  • Familiarity with rotational dynamics and moment of inertia
  • Knowledge of kinematics related to rolling motion
  • Basic algebra for solving equations
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  • Learn how to apply Newton's second law to rotational systems
  • Explore the relationship between linear and angular acceleration
  • Practice problems involving pulleys with mass and rolling objects
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Homework Statement




An green hoop with mass mh = 2.4 kg and radius Rh = 0.12 m hangs from a string that goes over a blue solid disk pulley with mass md = 2.4 kg and radius Rd = 0.11 m. The other end of the string is attached to a massless axel through the center of an orange sphere on a flat horizontal surface that rolls without slipping and has mass ms = 4.2 kg and radius Rs = 0.25 m. The system is released from rest.

1)What is magnitude of the linear acceleration of the hoop?


Homework Equations





The Attempt at a Solution



I have no idea, would love someone to explain all the very elementary steps, we have never even looked at taking the mass of the pulley into account!
 
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How would you solve it if the pulley were massless?
 

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