The rotating background is built on 2 gears as shown in Figure 1. Note in the figure that gear 2 and rotating body 3 have the same angular velocity but different linear velocities on the edges of the parts.

Figure 1. Rotating Background on Gear B setup where the vertical input gear is gear 1, the horizontal orange gear is gear 2 and the background is rotating body 3.

Gear 2 has twice as many teeth as Gear 1, which results in an angular velocity reduction on the scale of 1/2. In other words, for every rotation of gear 1, gear 2 only goes through half a rotation. This relationship is shown in the video below.

Various values for the Gear system are shown in Table 1.

Table 1. Gear Values

Body	Radius	N	Linear Velocity (in/s)	Angular Velocity (rad/s)
1	.805”	6	4.83	2π
2	1.315”	12	3.945	π
3	4”	N/A	12	π

The gear mechanism was easy enough to implement, but I had to add thicker card stock to Gear 2, its associated axle and the top of the box because the gears were not meshing properly. I had more difficulty when I added the background because it was very large and unstable. The background's movements affected the orientation of the horizontal gear below (gear 2), so I had to add a support layer below the backdrop to keep it level. The layer is yellow in the video below:

To re-emphasize the difficulty of continual gear meshing, I have added the following video. In the video, you can see how gear 2 shifts to the left and right depending on the wobble of body 3 instead of remaining vertical and meshing with gear 1.

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