A new physics toy in my house: A spinning top that has a pen as its tip and leaves trajectories as it spins!
The trajectories are really cool. Depending on how you spin the spinning top, they look really different. But they all have a common feature: When the spinning top has slowed down, they end in a long swivel away from all the neat spirals, and in the very end they have the small circle as seen in the top left corner of the picture below.
See? The radius of that circle is given by the distance from the tip of the pen to the point on which the spinningtop rests, hence it is the same for all the trajectories. But the rest? The trajectories that are really drawn out were those where the tray on which we were drawing was slowly tilted, so they went away from their point of origin, trying to go downhill.
Now if you don’t have such a spinning top, don’t despair. Use the stub of an old pencil (or of one from your favourite Swedish furniture place), pierce it, tip down, through a circular piece of cardboard, and there you go: Your drawing spinning top is ready!
Watch the movie at the bottom of this post to see this trajectory forming: