Speed of rotating, falling masses I'm having trouble understanding this problem that was on an AP Physics 1 sample questions page:

I know that the answer is C, but my question is: Why does the graph have those curves in it? Is it due to gravity changing the rotation speed, or tension, or what? It would be awesome if someone explained really clearly, since I am a physics beginner.
 A: 
Why does the graph have those curves in it? Is it due to gravity changing the rotation speed, or tension, or what ?

If you closely watch the center of the massless rod, which is the center of mass of the system, you will note that as soon as a ball goes "over the top" in its rotation, it is rotating toward the earth as it is falling, so its measured velocity is rapidly increasing.  When that ball passes the "bottom" of the circle that it is rotating through, it is falling towards the earth while rotating away from the earth, so the measured velocity is "flat" during this interval.  The ball on the other end of the stick is doing the opposite, so the measured velocities from the two balls are "out of phase" with each other, indicated by a "peak" from one ball and a "trough" from the other at certain instants in time.
Now, for my criticism of the problem.  Many problems in AP Physics 1 are written in a way that seems to be intended to show the cleverness of the question writer.  These questions are often at a very high conceptual level, and unfortunately, there are high schools where the students taking this course are seeing physics for the first time, so it is very difficult to get those students to think at such a high conceptual level.  In addition, many of the questions are ambiguous or have hidden assumptions in them, including the question that you posted.  The graph shows that the center of mass of the object is falling with a linearly increasing velocity, which indicates that the velocity measuring device is stationary with respect to the ground, but you don't get this information in the problem statement.  Obviously for a 1st year physics student, such information would be potentially helpful when said student is attempting to decipher the wording of the problem such that the underlying physics can be interpreted.
