A string is wound around a homogeneous, horizontal cylinder of mass M and radius R. The cylinder is then held above the ground and released from rest. As the string unwinds and the cylinder spins, the end of the string is continually pulled vertically upwards with a force that is just sufficient to keep the cylinder from descending to the ground. The figure shows the situation viewed from the side. (a) Identify the forces acting on the system (string and cylinder) and determine an expression for the tension in the vertical portion of the string. (b) Determine the angular acceleration of the cylinder. (c) What is the upward acceleration of any point along the vertical portion of the string?

A string is wound around a homogeneous, horizontal cylinder of mass M and radius R. The cylinder is then held above the ground and released from rest. As the string unwinds and the cylinder spins, the end of the string is continually pulled vertically upwards with a force that is just sufficient to keep the cylinder from descending to the ground. The figure shows the situation viewed from the side. (a) Identify the forces acting on the system (string and cylinder) and determine an expression for the tension in the vertical portion of the string. (b) Determine the angular acceleration of the cylinder. (c) What is the upward acceleration of any point along the vertical portion of the string?