We bought a spin art machine recently and busted it out yesterday. Noor noticed that when she spins the plate fast, the drops of paint run to the outside edge of the paper, but when she spins it slowly, the drop of paint forms a circle that doesn't radiate outwards. She asked why this was and we looked it up. Turns out it is due to Newton's First Law of Motion.
According to Isaac Newton, an object in motion will continue moving in a straight line unless acted upon by a force. The paint travels in a straight line once it is set in motion; it doesn't continue in motion indefinitely because it hits the edge of the paper or the edge of the spinner container.
When the force of the plate, which holds the paper, is less than the force of the rotation, the paint (which is constantly shifting the direction of its velocity) stays in a more-or-less solid line. When the force of the rotation is greater than the force of the plate, the drops are drawn outward.