The center-seeking force (centrifugal) of the spinning wheel has angular momentum. Angular momentum is conserved throughout a system and is transferred as a new center is found.
Cut a 15 cm disc out of the cardboard. The edges should be smooth. Draw a pattern on the disc. Make a hole in the center of the disc large enough for the pencil to slide through. Slide the disc to the middle of the pencil. (The disc should not slide on its own.) Next cut a strip of cardboard long enough to form a round ring from top to bottom around the pencil and around the disc. Draw several stripes (designs) across the strip. Form a ring by taping the ends together. Attach the top of the ring to the top of the pencil with a pushpin pushed carefully through the eraser. Allow enough of the pin’s top to stay above the ring to hold with your finger tips. The bottom of the ring can be held in place by the pencil lead. The ring should rotate around the pencil but stay connected. The pencil will serve as the main axis. Now quickly spin the pencil between your fingertips and let the lead end touch the table top. Observe the motion of the pencil, disc and the ring. Compare the motion of each as the system spins. Does each part spin the same?
A smaller version of this can be shown using a gyroscope (children’s toy). At high speeds the gyroscope is very stable. When it slows or leans, it tries to correct itself and causes a wobbling effect. An even more simple example is the cardboard wheel attached to a string. When spun quickly the wheel appears to hover (rotate) around the string. What other motions do you observe?