We have now been introduced to the fundamental angular variables: the angular displacement q (theta), the angular velocity w (omega), the angular acceleration a (alpha), and the angular version of force—the torque, t (tau).  We have seen that there are relatively straightforward relationships between the linear variables and the corresponding angular variables:

(linear quantity) = r (angular quantity)

For example, x = r q , v_t = r w , and a_t = r a . The torque equation changes the format slightly: t = r_perp F.

We shall now go on to define the remaining angular quantities in rotational dynamics, and see that a simple translation exists between the linear  relations and the corresponding angular relations. Indeed, some of the angular definitions were made simply to make the resulting relations among the angular variables look like the corresponding linear relations with which we are already familiar!

We start off with a discussion of inertia, both linear and rotational. We then move on to other relations, pretty much in the order in which we encountered the linear quantities. The last section of this lecture gives a table which summarizes the linear and angular quantities and relations among those quantities.