A children’s stacking rainbow toy easily demonstrates the motion of a rocking semicylinder or semicylindrical shell. This toy provides a simple way to discuss how the period of an oscillating object depends on the location of the center of mass and the moment of inertia about the ground. Here, I develop the theory for the period of a rocking semicylinder and a rocking semicylindrical shell. The theory agrees well with experimental evidence of the period of the rocking rainbow.
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