Let's look at some limiting cases as a way to build your intuition and also to check your answers. If you can't answer these questions now, work through other parts of this problem first and then consider these special cases using your final analytic answer. In the limit that the moment of inertia I→0 while the mass m remains finite, what magnitudes would you expect for the tension T in the vertical section of string and the downward acceleration a of the center of mass? Note: This is a hypothetical cylinder with all its mass concentrated along its axis. The rest of the cylinder (i. e. the bulk) is massless.

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.