How Do You Calculate Force and Work for a Suspended Spool in Rotational Motion?

AI Thread Summary
To calculate the force exerted on a suspended spool of thread, one must consider the balance of forces acting on it, ensuring that the upward force equals the weight of the spool. The work done on the spool as it unwinds and reaches an angular velocity w can be derived from the kinetic energy equation, which combines both rotational and translational components. A free body diagram can help visualize the forces involved, including tension and gravitational force. Understanding the relationship between these forces is crucial for solving the problem accurately. The discussion emphasizes the importance of applying the correct formulas and concepts to determine the force and work involved in the spool's motion.
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Homework Statement


A narrow but solid spool of thread has radius R and mass M. If you pull up on the thread so that the CM of the spool remains suspended in the air at the same place as it unwinds,
(a) what force must you exert on the thread?
(B) how much work have you done by the time the spool turns with angular velocity w?


Homework Equations



k=1/2Iw^2 + 1/2MR^2w^2



The Attempt at a Solution



I've tried to make an understanding that when your pulling upward for problem (a) you are canceling out the force being put on the spool. by pulling up. I'm just having trouble trying to find the correct formula to use to find Force. any help in the right direction would be great.
 
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Draw a free body diagram of the spool. How many forces act on the spool? How must these forces be related if the spool remains suspended in air, i.e. its center of mass does not accelerate?
 

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