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.

For her birthday, my 4-year-old daughter got the stacking rainbow toy shown in Fig. 1. This toy is made of several different bent pieces of wood that fit inside each other and are painted to mimic the colors of a rainbow.1 In addition to providing opportunities for children to build with the curved pieces, this toy can be inverted and tilted slightly and then released to show an object...

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