This paper describes a set of experiments aimed at overcoming some of the difficulties experienced by students learning about the topics of moments of inertia and simple harmonic motion, both of which are often perceived to be complex topics amongst students during their first-year university courses. By combining both subjects in a discussion about "physical pendula", in which the oscillation time periods for the periodic motion of several objects (a tennis ball, a thin beam, a hoop and a solid disc) are measured and compared, students are able to understand both topics at a higher level and also experience the synergistic effect of combining two or more physics themes in order to accelerate their learning whilst simultaneously raising their motivation. Special attention is given to the "ball and stick" pendulum in which a block of material (treated as a point mass) can be moved along a shaft to create a composite pendulum whose time period exhibits a minimum value at a certain separation between the block and the rotation axis. (Contains 1 table and 6 figures.)