In this video the bicycle wheel is all ready spinning when the movie starts. Notice that is does not fall. It is rotating around because of the pull of gravity. (Far away from the Earth, where there is nearly no effect due to the gravitational pull of the Earth, the wheel will sit in space without rotating.) At the end of the video the wheel is stopped and gravity easily pulls it down.

This video can be found on YouTube at https://youtu.be/xhn3H4Aqgpg

This girl is sitting on the spinning stool. She is holding onto the back of the stool so she will not fall off. At first her mass if far away from the center. When she pulls in her hands and legs the mass is closer. Notice how the rate that she spins changes.

When an object is spun, it is given and certain amount of rotation inertia. It does not want to loose this inertia because inertia resists a change in motion. When the mass's position is changed, the rate of spinning also changes to make sure the amount of rotational inertia is maintained. You can see this in the video above.

This is a great one minute video by Paul Hewitt Explaining why you do not need to hold the toilet paper to rip it off.

A roll of paper towels experiences the same physics.