Gears and pulley systems — study worksheet

1. Read the core idea

Two directly meshed external gears turn in opposite directions. Gear tooth counts determine relative rotational speeds: the smaller gear turns faster when meshed with a larger one. An intermediate gear can change direction without changing the overall speed ratio between the first and last gears. For ideal pulleys, distinguish a direction change from a force advantage by counting rope segments supporting the moving load.

2. Trace the worked example

A 20-tooth gear driving a 40-tooth gear makes the larger gear turn at half the speed in the opposite direction.

Write the steps or relationships that explain the result:

3. Use the method

Trace one connection at a time; label direction separately from speed or force.

Summarize the method in your own words, with a diagram or labeled units where useful:

4. Record a mistake to avoid

One fixed pulley changes pull direction but does not ideally halve the required force.

Describe how you will recognize and correct this mistake:

5. Review after practice

Use the mixed practice check linked in the hub. Record the skill you need to revisit and your next study step.