Derive formula for resulting horizontal acceleration


A cord is wrapped around spool of inner and outer radii r and R respectively. The spool of mass m and radius of gyration rests on a flat rough horizontal surface and does not slip whenever it is in rolling motion. Force F is applied to the cord inclined by angle to the surface. Derive formula for resulting horizontal acceleration of the spool's mass center. Explain in words meaning of positive and negative values of .

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Mechanical Engineering: Derive formula for resulting horizontal acceleration
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