Given that gear X has 5 teeth and is connected to a motor, gear Y has 20 teeth as an intermediate idler, and gear Z has 30 teeth connected to the roller, what should be the motor's speed if the roller requires 50 rpm?

To determine the correct motor speed, we need to analyze the gear ratio involved in the setup. The configuration consists of three gears: gear X connected to the motor, gear Y as an idler, and gear Z connected to the roller.

The relationship between gear speeds is determined by the number of teeth each gear has. The gear ratios dictate how the speed translates from one gear to another.

1. Gear X to Gear Y: Gear X has 5 teeth, while Gear Y has 20 teeth. The gear ratio from X to Y is 5:20, or simplified, 1:4. This means for every rotation of gear X, gear Y will rotate 1/4 of that rotation.

2. Gear Y to Gear Z: Gear Y has 20 teeth and Gear Z has 30 teeth. The gear ratio from Y to Z is 20:30, or simplified, 2:3. This means for every rotation of gear Y, gear Z will rotate 1.5 times (or 3/2 of the rotation).

Now, we can calculate the overall effect from motor to roller:

• If gear Z needs to turn at 50 rpm, we can find out how fast