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 |