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The spool has a mass, m, and a radius of gyration kG. An inextensible cord is attached to the wall at point A, and is wrapped around the inner portion of the spool. The inner radius is R and the outer radius is 2R. The coefficient of friction between the spool and the ground is mu. The instantaneous center of zero rotation is located at point C.Find Fcrit (the force needed to cause motion) applied at point B.If the force is increased to 2Fcrit what is the linear acceleration of the center of mass?If the force is 2Fcrit what is the tension in cord AC?

Question

The spool has a mass, m, and a radius of gyration kG. An inextensible cord is attached to the wall at point A, and is wrapped around the inner portion of the spool. The inner radius is R and the outer radius is 2R. The coefficient of friction between the spool and the ground is mu. The instantaneous center of zero rotation is located at point C.

  • Find Fcrit (the force needed to cause motion) applied at point B.
  • If the force is increased to 2Fcrit what is the linear acceleration of the center of mass?
  • If the force is 2Fcrit what is the tension in cord AC?
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Step 1

The equations of motion are,

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Step 2

For F = Fcrit,

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Step 3

Therefore...

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Physics

Rotational Mechanics

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