One morning my son began amusing himself by rolling the peanut butter lid across the breakfast table. Of course, little sister wanted in on the fun, so we retrieved the orange juice lid as well.
The orange juice lid did something new. It rolled in a circle.
When I asked my kids why the peanut butter lid was traveling in a straight line, while the orange juice lid traveled in a circle, my son was able to tell me that it was because the outside rim of the orange juice lid is longer than the inside rim.
He was right! As a solid object, the entire lid must maintain the same angular speed. Every molecule revolves around the center at the same speed. For the peanut butter lid, which has a uniform circumference, that means that all parts of the lid travel at the same linear speed as well. However, for the orange juice lid, the smaller circumference on the inside means that a smaller linear distance will be traveled on the inside of the lid during each rotation. In order for a solid object, like the lid, to travel a smaller linear distance on one side than the other, it has to travel in a circle.
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