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Science Museum

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, look around to make sure no one's watching, 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 decisions. For example, if you wanted to make the red gear spin as fast as possible, would you spin the large blue gear or the small green gear?

Try spinning both gears to see if you made the right choice.

Learning to apply mathematics in real-world situations like these is a great way to prepare for exams.