The rotation axis of the uniform cylinder is  constrained by a frictionless slot. The cylinder is at  rest when it is lowered onto the conveyor belt, which  has a constant translational velocity of 20.0 ft/s. The  coefficient of friction between the belt and the  cylinder is 0.400. a) Calculate the maximum angular velocity of the  cylinder. b) The distance traveled by the belt during the time  the cylinder is accelerating to its maximum  angular velocity

The arms of a Hartnell governor are of equal length. When the sleeve is in the mid- position, the masses rotate in a circle with a diameter of 150 mm (the arms are vertical in the mid-position). Neglecting friction, the equilibrium speed for this position is 360 rpm. Maximum variation of speed, taking friction into account, is to be 6% of the mid- position speed for a maximum sleeve movement of 30 mm. The sleeve mass is 5 kg and the friction at the sleeve is 35 N. Assuming that the power of the governor is sufficient to overcome the friction by 1% change of speed on each side of the mid-position, find (neglecting obliquity effect of arms), the (i) mass of each rotating ball (ii) spring stiffness (iii) initial compression of the spring