Elite097 wrote:
ThatDudeKnows how is speed related to circumference here and why does it lead to halving? I easily think speeds can be different for two gears as well even though one has half the diameter as another and they are connected
avigutman Elite097 Measuring the speed of a rotating gear is tricky because it's not actually moving anywhere - it stays in place.
The typical way to measure the speed of rotation, therefore, is using units of
rpm (revolutions per minute): measuring how many full circles (360 degrees) the gear does in 1 minute. But, what is a "full circle", or, revolution? If you mark a point on the top of the circumference of the gear, a full revolution is complete when that point comes back to the top of the gear. In other words, the whole circumference of the gear would have passed through the top. For example: The second hand of a conventional analog clock rotates at 1
rpm.
Another way to measure the speed of rotation is to measure the movement of the point you marked at the top of the gear. That point will travel the full circumference of the gear in every revolution. So, if a gear with diameter
d rotates at a speed of 6
rpm for example, the point you marked will travel a distance of 6*(pi*
d) per minute. What if you double the circumference? How would that impact the point's speed, if you keep the gear's
rpm the same? Conversely, if you want the point's speed to remain unchanged, what must you do to the gear's
rpm when you double its circumference?
In this question, we have 2 gears that interlock. What does that mean? Here's a
visualization. If one gear has twice the circumference of the other, it must rotate half as many times per minute. Why? Well, if you mark a little dot every inch along each of the circumferences, the big gear will have twice as many such dots. However, since the gears interlock, the dots on the two gears must be moving at the same speed. If your gear has twice as many dots, and those dots are moving at the same speed as the dots on my small gear, then your dots have to travel twice the distance and will take twice as long to complete their journey of a full revolution. Therefore, your gear must be doing half as many revolutions per minute as my gear.