The 30 kg spool of outer radius ro= 450 mm as a centroidal radius of gyration k ? = 275 mm and a central shaft of radius ri=200 mm

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The 30 kg spool of outer radius ro= 450 mm as a centroidal radius of gyration k ? = 275 mm and a central shaft of radius ri=200 mm. The spool is at rest on the incline when the tension T = 300 N ,being parallel to the incline, is applied to the end of a cable which is wrapped securely around the central shaft as shown. The coefficients of frictions of the are μs= 0.45 and μk = 0.30.

The incline slop is θ =20°

Assuming the spool is rolling up the incline, draw the free body diagrams of the cylinder, showing the equilibrium of external and inertia forces

Assuming rolling with no slip, write down the equations of dynamic equilibrium and determine the acceleration of the mass center of gravity, point G and the angular acceleration of the spool.

Assuming slippage occurs, determine the acceleration of the mass center of gravity, point G and the angular acceleration of the spool.

Considering the maximum friction force that can be exerted by the ramp on the spool, which assumption is correct: rolling with no slippage or rolling with slippage.