Gears: Ratios, Proportions, and Linear Relationships

Pre-Lab

1. Watch as your teacher shows some gears turning. Do the gears turn in the same directions? Do they move at the same speed?

2. What are gears? What do gears do?

3. A gear train is a group of two or more gears that interlock and rotate together. What would happen if the teeth of gears in a gear train were not the same size?

4. List at least two devices that you use that operate with gears.

5. On the Lego device, notice that the gear attached to the hand crank “pushes” the other gear. A gear attached to a hand crank or motor is called the driver gear or input gear. A gear that is pushed is called a driven gear, follower gear, or output gear. How many times does the follower gear turn if you make the driver gear turn one complete revolution?

Driver (input) gear: 1 revolution Follower (output) gear: revolutions

6. The relationship between the driver gear and the follower gear can be expressed as a ratio. Ratios look like fractions. The gear ratio is always expressed as input motion over output motion. For example, a 36-tooth driver gear is matched to an 18-tooth follower gear. One revolution of the driver causes 36 of its teeth to mesh with 36 teeth of the driven gear. This is 36/18 = 2 ´ the driven gear’s teeth. Therefore the driven gear must turn 2 times. The gear ratio is:

You can also count revolutions directly, instead of teeth. In this example, when the driver gear makes 1 revolutions, the follower gear makes 2 revolutions, so

Calculate the own gear ratio with the number of revolutions you counted for the driver and follower gear. Remember, gear ratio is always input gear (driver) over output gear (follower, driven).

7. How can you use the gear ratio to predict the number of follower gear rotations?

8. A proportion is an equation showing that two ratios are equal. You can use proportions to predict the number of rotations of a follower gear for any number of driver gear rotations. How many times will the follower gear rotate if the driver gear turns two rotations? Write your prediction in the middle column of the data table below.

9. Using the gear ratio you calculated in step 6, predict how many rotations the follower gear will make for two, three, and four turns of the driver gear. Enter your predictions in the middle column of the table below. (You will fill in the last column later by counting the rotations.)

Rotations of Driver Gear / Predicted Rotations of Follower Gear / Actual Rotations of Follower Gear
2
3
4

10. Now turn the handle two, three, and four rotations and count the rotations of the follower gear. Fill in the actual number of rotations in the last column of the data table. Were your predictions correct?

11. Graph the number of rotations of the driver gear vs. the number of rotations of the follower gear.

12. Looking at the graph, predict how many times the follower gear will rotate if the driver gear turns five rotations.

13. Notice that the graph is a line. What do you call this kind of relationship? What does the graph tell you about the rate of change for follower gear rotations compared to the driver gear rotations?

Gears: Pre-Lab Student Notes Page 4 of 1