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The Uses of Math
How does trigonometry apply in real life? You might be wondering that yourself. Thinking when hell am I ever going to use trigonometry. One of the hundreds of ways you can use it is to determine the most efficient gear ratios either for cars or for bikes. When I say efficient I mean either fuel efficient, or the most acceleration, or the highest top speed, or combination of all of those things.
You see gears in just about everything that has spinning parts. Car engines and transmissions contain many gears. So how do they work? Gears are generally used for one of four different reasons: To reverse the direction of rotation, to increase or decrease the speed of rotation, to move rotational motion to a different axis, and to keep the rotation of two axes synchronized. The fact that one gear is spinning twice as fast as another is because of the ratio between the gears; the gear ratio. If the diameter of a gear is twice that of another gear, the gear ratio is 2:1. Every time the larger gear goes around once, the smaller gear goes around twice. If both gears had the same diameter, they would rotate at the same speed. Understanding the concept of the gear ratio is easy if you understand the concept of the circumference of a circle. Keep in mind that the circumference of a circle is equal to the diameter of the circle multiplied by Pi. Therefore, if you have a circle or a gear with a diameter of 1 inch, the circumference of that circle is 3.14159 inches. The circumference of a circle with a diameter of 1.27 inches is equal to a linear distance of 4 inches.
Most gears that you see in real life have teeth. The teeth have three advantages: They prevent slippage between the gears. Therefore, axles connected by gears are always synchronized exactly with one another; they make it possible to determine exact gear ratios. You just count the number of teeth in the two gears and divide. So if one gear has 60 teeth and...
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