A uniform solid cylinder with mass ?M? and radius 2?R? rests on a horizontal tabletop. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can rotate about the axle. The string runs over a disk-shaped pulley with mass M and radius R that is mounted on a frictionless axle through its center. A block of mass M is suspended from the free end of the string (?Fig. P10.75?). The string doesn’t slip over the pulley surface, and the cylinder rolls without slipping on the tabletop. Find the magnitude of the acceleration of the block after the system is released from rest.
Solution 87P Introduction We have to calculate the acceleration of the mass hanging. Step 1 The following figure shows the free body diagram of the each component.