The Loop the Loop track can be reintroduced here, and the rotational energy of the rolling ball added to the calculation of the height that the ball must be released to just make it around the track. Note that the ball does not ride on its bottom, but partly up on its sides. You will still need to add in "a couple of inches of friction." (See Loop the Loop (Energy) [1])
Various objects are raced down an inclined plane. There are two sets of disks, one with the mass distribution concealed and the other with the mass distribution apparent. All of the three inch disks have the same mass which you can demonstrate by placing two at a time on a double pan balance. There are also a few smaller disks available so you can demonstrate that disks of the same mass distribution but different sizes and masses roll the same.
Unidentified Rolling Objects (Audience Appeal)
These demonstrations are often shown with the rolling objects above, or on the first day of class, or at physics demonstration shows, to attract interest in physics, and as an illustration scientific reasoning in working out their mechanism "How would you design a mechanical system to do this?"
One of the "unpredictable disks", shown above, rolls down and one rolls up. The off-center weight is concealed from the audience, but can be shown after they have tried to reason out the mechanism. A "prematurely-stopping cylinder" rolls part way down and stops. A "come-back disk" rolls down some distance, and then rolls back up!
This simple device graphically illustrates the concepts of torque and rotational inertia. Movable masses are positioned on a rod which is rotationally accelerated by a falling weight. The rod arm accelerates rapidly when the masses are moved in toward the center but much more slowly when the masses are adjusted out to the ends of the rods so that the rotational inertia is large. Two devices are available so that the class can directly compare the cases of large and small rotational inertia.
The Position of masses on rods can be varied to change the rotational inertia of a torsion pendulum. The period of the pendulum is longer for larger moments of inertia. The torque of the support wire accelerates the rotational motion more slowly when the rotational inertia is large. (See Simple Harmonic Motion [2])
Illustrates how changing the rotational inertia changes the angular velocity. (See Turntable and Weights (Angular Momentum) [3])
Links:
[1] https://demoweb.physics.ucla.edu/node/397
[2] https://demoweb.physics.ucla.edu/node/261
[3] https://demoweb.physics.ucla.edu/node/380