Question

The spool has a mass, m, and a radius of gyration k_{G}. 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 F
_{crit}(the force needed to cause motion) applied at point B. - If the force is increased to 2F
_{crit}what is the linear acceleration of the center of mass? - If the force is 2F
_{crit}what is the tension in cord AC?

Step 1

The equations of motion are,

Step 2

For *F* = *F*_{crit},

Step 3

Therefore...

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