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An 8 lb. block slides on a horizontal table; between the block and table, coeffecient of friction = 0.25. The block is pulled by a string over a light, frictionless pulley wrapped around a solid cylinder of radius 2 ft. and weight 8 lb. The cylinder is released from rest. Compute the acceleration of the block and the tension of the string.

The falling cylinder is basically like a yo-yo.

The tension on both sides of the pulley are the same

I've taken the torque about the center of the cylinder:

Tension in the string = (mass cylinder)(tangential acceleration)/2

I've also used Newton's Second Law with respect to the forces in the horizontal direction for the block and vertical direction for the cylinder.

What I'm having trouble with is the relationship between the different accelerations in these equations.

The cylinder is falling and unrolling. The acceleration that's referred to when you use NSL on the falling cylinder is the acceleration of the point where the string is unwinding, right? But how is this related to anything?

Any hints would be greatly appreciated.

Thanks.