Mathematics in Science
You reach the end of the hallway with the murals and proceed into an interactive section of the museum. One table demonstrates gear ratios.
You walk up to the table, feeling relaxed and self-assured, and turn the crank attached to one of the gears. It feels a little silly, but sure enough, all of the other gears begin to rotate at different speeds. A sign helpfully explains the phenomenon.
The speeds of any two interlocking gears, assuming no friction or backlash, are always directly proportional to each other. In other words, they obey the equation X = Y * C, where X and Y are the rotations each gear makes per minute and C is a fixed constant.
Scientists use equations like these to make predictions. For example, try spinning the blue gear so that it makes five rotations every minute. Notice that the red gear rotates twice as quickly, making ten rotations per minute. What do you think will happen if you spin the blue gear twenty times per minute?
Test out your prediction to see if it was correct.
Learning to apply mathematics in real-world situations like these is a great way to prepare for exams.