"The Hall car of mass m-c is connected to mass m-2 by a string as shown in the figure below. The string passes over a solid cylindrical pulley, which has a frictionless bearing of radius R and mass M. When the system is released from rest the string does not slip, the Hall car moves down the incline, and m-2 moves upwards through a distance h'. Derive an expression for the translational acceleration of the masses in terms of m-c, m-2, M, h', 2, and the coefficient of friction U." (I suspect that the term "2" might be a typo for theta; however, even with that assumption I can't solve in terms of h'). The figure is simply a right triangle with the car descending a distance h' along it's hypotenuse and m-2 ascending along it's verticle leg a distance h'. Theta is the angle opposite to the verticle leg and at the top of the verticle leg is the pulley. Finally, there is a friction arrow from the car directed opposite the direction in which the car is descending. Tried these equations after finding the Net Force on the car, block and pulley: Torque= Tension times radius= Moment of Inertia times Angular Acceleration= (.5MR^2)(a/R)= (.5MRa). Also PE= KE. I was unsuccessful using the energy conservation approach, i.e., the PE of the car= the KE of the car and the rotational KE of the pulley. With the Newtonian approach: a= 2[(m-c)(g)(sin8)-(U)(m-c)(g)(cos8)-(m-c)(g)]/[M+(m-c)+(m-2)]. This solution is not in terms of h'. Moreover, it is in terms of the seemingly unavoidable g and theta.