In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 1.00 m so r = , and, while being driven into rotation around a fixed axis, its angular position is expressed as a = b = where u is in radians and t is in seconds.
(a) Find the maximum angular speed of the roller.
(b) What is the maximum tangential speed of a point on the rim of the roller?
(c) At what time t should the driving force be removed from the roller so that the roller does not reverse its direction of rotation?
(d) Through how many rotations has the roller turned between t = 0 and the time found in part (c)?