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

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SUMMARY

The discussion focuses on calculating the force exerted on a suspended spool of thread and the work done as it rotates. The spool has a radius R and mass M, and the relevant equation for energy is k = 1/2Iw² + 1/2MR²w². To maintain the spool's center of mass in a stationary position while unwinding, the upward force must equal the gravitational force acting on the spool. The participant seeks clarification on the correct formula to determine the force and emphasizes the importance of analyzing the forces through a free body diagram.

PREREQUISITES
  • Understanding of rotational motion and angular velocity
  • Familiarity with the concepts of force and work in physics
  • Knowledge of moment of inertia (I) and its calculation
  • Ability to draw and interpret free body diagrams
NEXT STEPS
  • Study the relationship between linear and angular motion in physics
  • Learn how to calculate moment of inertia for various shapes
  • Explore the principles of work-energy theorem in rotational dynamics
  • Practice solving problems involving free body diagrams and forces in equilibrium
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Students studying physics, particularly those focusing on mechanics, as well as educators and tutors looking to enhance their understanding of rotational motion and force calculations.

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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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