In the last section we discussed rotating objects in the context of kinematics. We now must ask how objects come to rotate. Immediately after our early discussions of kinematics near the beginning of the course, we discussed forces. The reason for that was that forces are responsible for the acceleration terms which arise in kinematics equations. The connection was of course that [math]\sum\vec{F}=m\vec{a}[/math] through Newton's second law.[br][br]It turns out that the application of a force is not sufficient to induce a rotation in an object. Instead, it also depends on how the force is directed. This leads to the discussion of torque, which can be thought of as a "twist". The more effective the twist, the larger the torque. [b]Torque applied to an object induces an angular acceleration. [/b]If it helps, the cause and effect sequence may be seen as: Torque ->angular acceleration -> angular velocity ->rotation. This is in contrast with our earlier studies in which the sequence was: Force -> linear acceleration -> velocity -> translation.[br][br]The other thing that we will need to discuss is that Newton's second law for rotating objects does not just need a torque to replace the force and an angular acceleration to replace the acceleration. Rather, the mass needs to be replaced as well. While a big mass is harder than a little one to get rotating, it is also very important to know how the mass is distributed. In other words, the shape of the object matters when we wish to rotate it. That aspect didn't matter when inducing a linear acceleration. The mass, along with how it is distributed, combine to give a measure of how hard it is to get a certain object rotating, or to stop it once already rotating. That term is called the[b] rotational inertia[/b].

Once we discuss torque and rotational inertia, the only things left to do are to discuss work, energy and momentum for rotating systems. In that sense we will in a single chapter apply to rotating systems what took a good part of a semester to develop for translating systems. Since you already know those concepts and definitions, it will not be too hard.