The spool has an inner radius ot r and an outer radius ot R When the spool is pu

Question

The spool has an inner radius ot r and an outer radius ot R When the spool is pulled by a Tension Force as shown in the figure, it was shown iu lecture demo that the CM of the spool can move forward or backward depending on the angle theta. You are asked to analyze the problem and determine the critical angle thetac that determines which way the spool will move. assumptions The spool rolls without lipping m all cases. The spool always stays in contact with the floor, i.e. the component of the acceleration of CM iu the vertical direction is always zero, which means that there is a condition on how large the applied tension force can be. The tension rope unwraps from the inner axle without any slipping.

Explanation / Answer

lets treat this problem with the axis perpendicular to the contact point. as you can see. there are 4 forces. weight, normal force, friction force and tension. the first 3 force have their direction go through contact point. so they dont cause any torque. T=T*(R*sin0-r) (take counter clockwise to be positive). so critical angle is when sin0=r/R if sin0>r/R then T is positive, so it ll go to the left and vice versa

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