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Odd Ball

a motorized ball rolls around in a container
Set it down and watch it roll around randomly.
a motorized ball opened so you can see the motor inside
If you look inside, you can see there is a motor that turns.

Place the ball in an enclosure, and it will appear to roll around randomly. It helps to place an object or two in the enclosure for the ball to bump off of, otherwise it may just follow the edge, which is not so interesting. There is a motor inside, which shifts the center of mass of the ball as the motor rotates, causing the ball to roll. If the ball is oriented just right, it can roll in a line.

There's actually some really interesting math at work here. One is that, most of the time, the axis of the motor and the axis of rotation of the motor are not aligned, so there is a mixing of different types of rotation. The complicated motion that you see is because of what a mathematician would call the noncommutativity of the rotation group. In plainer terms, a rotation followed by another rotation (around a different axis) is equivalent to an overall rotation around a completely different axis, in a way which may not be intuitively obvious. Two is that as the sphere rolls, you can think of it as unwrapping a sphere along a plane, which as you know from looking at different attempts to draw a flat map of the Earth, is complicated by the curvature of the sphere.

Materials

  • The motorized ball (sometimes listed as "cat in a bag")
  • some type of enclosure, with one or two objects to break up the space

Construction Instructions

There's not much to do, other than removing the extra stuff that comes attached to the ball in some kits. Prepare the enclosure. Remember to disconnect the battery when the ball is not in use. We usually just remove it from the battery compartment then just drop it into the sphere before screwing it shut again.