A large 16.0-kg roll of paper with radius R = 18.0 cm rests against the wall and is held in place by a bracket attached to a rod through the center of the roll (?Fig. P10.61?). The rod turns without friction in the bracket, and the moment of inertia of the paper and rod about the axis is The other end of the bracket is attached by a frictionless hinge to the wall such that the bracket makes an angle of 30.0O with the wall. The weight of the bracket is negligible. The coefficient of kinetic friction between the paper and the wall is µk = 0.25. A constant vertical force F = 60.0 N is applied to the paper, and the paper unrolls. What is the magnitude of (a) the force that the rod exerts on the paper as it unrolls; (b) the angular acceleration of the roll?

Solution 69P We shall have to first calculate the normal reaction exerted by the roll on the rod. Once this force is known, we shall have to calculate the torque and then the angular acceleration of the roll. Let us have a look at the following free body diagram. Let R be the normal reaction exerted by the roll on the rod. R be the normal reaction 1 2 of the wall on the roll. The force of friction will act downward as the roll will rotate clockwise. If we resolve the components of R , 1 0 R =2R sin130 …..(1) 0 R c1s 30 = Weight + Friction...