Hi I have the following homework problem that I need to solve two times, one time using forces / torques / acceleration and again using work and energy. I have attached a diagram of the problem and the variables. Pertaining to the first method, I think the solution could be achieved by the following... ( The friction of the pulley is neglected, but the connecting strin does not slip ) ( Angular acceleration will be represented by a<ANG> ) Starting from Newton's Second law, F = m * a The equations for the block on the table and the hanging block are as follows... (T is the tension of the string) <table block> T - fk = m<table> * a <hanging block> T - m<hanging> * g = m<hanging> * a The torque of the pulley is: (I is the rotational inertia) Torque<NET> = I * a<ANG> which equates to: -R * T = 1/2 * M<pulley>(r^2 + R^2) * a<ANG> (R is negative because it's moving in a clockwise direction. I is rotational intertia of an annular cylinder) To eliminate T, the net force equation for the table block is solved for T: T = m<table> * a + coeff-kin * m<table> * g I'm not really sure which direction to go after this, or if this is even correct. I think I need to substitute the above equation for T into the annular cylinder equation, but that doesn't look like it works out corectly. Anyone have any ideas? Thanks in advance for any help.