We have now seen how to relate the kinematic quantities describing a particle’s motion when there is a constant acceleration, and we have seen how this constant acceleration is  related to forces by means of Newton’s three laws of motion, in particular the second law which directly relates the forces acting on the object to the resulting acceleration of the object.

We are now about to undertake a description of a very special kind of motion, but a very important one: uniform circular motion.  Our discussion of this topic will apply many of the concepts that we’ve encountered so far in this course with the addition of what is really just a few new definitions.

Warning: This material tends to be very confusing for many students.  The reason for this confusion seems to stem from a conceptual misunderstanding of the fundamental concepts of velocity and acceleration,  coupled with people really not believing Newton’s 1st law (do you remember which one that is?), no matter how much they say they do.  (See the discussion of Newton’s three laws at the beginning of L8 if you need a refresher.  Actually, this would probably be a good idea even if you don’t think you need a refresher!)

Consider the following.  You are riding in the back of a big bus with a bunch of other people. You are riding down a long, straight road, and everyone in the bus is sitting up and talking with one another.  Suddenly, there is an unexpected and rather tight curve in the road to the right, and the bus driver dutifully turns the bus sharply to the right.  As you are making the turn, you notice everyone in the bus leaning.  In which direction are they leaning?  To the left, of course — away from the curve (or, more precisely, away from the center of the curvature in the road).  Why is this?  You can only deduce that this is because there is now a force acting on the people in the bus that wasn’t acting before, and which is a result of the curved path now followed by the bus. In which direction does this force act on the people in the bus? Think about it, and jot down your answer along with a short reason of why you think this is the answer.  (OK — you don’t have to do this, but it wouldn’t be a bad idea just to help you get over any possible misconceptions with this material!)

The typical answer that people (physics students or not!) give to the question above is that there is now a force acting to the left on the people in the bus as a result of the curved motion followed by the bus. This answer is wrong.  There is actually a force acting on the people to the right which results in their bodies leaning to the left!  If your answer was correct then congratulations — you are in the great minority. If your answer was wrong, then don’t fret. We’ll be spending more time with this discussion soon... (see the section on Centripetal Force in this lecture).

The next section will introduce you to some definitions (some possibly old, some new) that will be important for this as well as later lectures. We will then go on to discuss the all-important and elusive centripetal force....