What is the ratio of the driven gear to the driving gear if the driven gear has twice the number of teeth?

When determining the ratio of the driven gear to the driving gear, it's essential to understand the relationship between the number of teeth on each gear. In this case, where the driven gear has twice the number of teeth compared to the driving gear, you're looking at a scenario where the driving gear is the one providing motion.

For example, if the driving gear has a certain number of teeth, say ( x ), then the driven gear, having twice as many teeth, would have ( 2x ). To find the gear ratio, you compare the number of teeth on the driven gear to that of the driving gear. The ratio can be expressed as:

[ \text{Ratio} = \frac{\text{Number of teeth on driven gear}}{\text{Number of teeth on driving gear}} = \frac{2x}{x} ]

This simplifies to 2, which indicates that for every 1 turn of the driving gear, the driven gear will turn 0.5 times, or vice versa, the driven gear rotates slower but with greater force due to the extra teeth. Thus, the correct way to express the ratio of the driven gear to the driving gear is two to one.

This understanding is fundamental in gear