Gears and Speed Investigation

In this investigation we explored the relationship between gearing up or gearing down and speed.
We were testing two hypotheses used to predict this relationship; the first being:

A: Speed One/Gear Ratio One = Speed Two/Gear Ratio Two
and the second being:

B: Speed 1 * Gear Ratio 1 = Speed 2 * Gear Ratio 2

We then setup our taskbot to run for 3 seconds and recorded the distance the robot moved each time with three different gear ratio configurations, 1:1, 3:5, and 5:3. Following this we used each formula to predict the speed at which the robot would travel at each speed, later comparing this to the actual angular velocity at which the robot moved by dividing the distance by the time (3 seconds). After comparing all of the results we found that hypothesis B was very accurate in predicting the actual speed the robot would go. Looking at the values produced by our experiment we found that the relationship between gear ratios and speed is inverse. Inverse meaning that as the gear ratio decreases, the speed increases, and as the the gear ratio increases, the speed decreases. This relationship is the opposite of a direct relationship such as that between wheel size and distance.