  The study of the motion of a rigid body on a plane (RBP motion) is usually
one of the most challenging topics that students face in introductory physics
courses. In this paper, we discuss a couple of problems which are typically
used in basic physics courses, in order to highlight some aspects related to
RBP motion which are not usually well understood by physics students. The first
problem is a pendulum composed of a rod and disk. The angular frequency of the
pendulum is calculated in two situations: disk fixed to the rod and disk free
to spin. A detailed explanation of the change in the angular frequency from one
case to another is given. The second problem is a ladder which slides touching
a frictionless surface. We use this problem to highlight the fact that the
contact forces applied by the surface perform translational and rotational work
despite that the total mechanical energy of the ladder is conserved.
