Gears: The gear is one of the oldest mechanical devices. It has been used since ancient times for its ability to increase or decrease rotational velocity. When one gear turns another, the outer portions of the gears are turning at the same linear speed. However, when one gear is smaller or larger than the other, the speed of rotation will be different for each gear. Let's look at an application of gears that you've seen before. On a bicycle the pedals are attached to a large gear at the center of the bike, and a chain connects the large gear to a small gear attached to the rear wheel. The chain does not change speed of rotation, it serves only to separate the centers of rotation.
Consider a bicycle where the large central gear has a radius of 4 inches and the small back gear has a radius of 2 inches.
Part A: How many inches would a point on the outer edge of the large gear travel in a 150 degree rotation?
Part B: What degree of rotation will the small gear undergo when a point on its outer travels the same linear distance determined in part A?
Part C: If the center of the small gear is rigidly attached to the seneter of a bicycle wheel with a radius of 10 inches, how many inches will the bicycle travel with a single rotation of a large gear?
Part D: How does the distance you determined in part C change if the radius of the small gear is 1.5 inches and the radius of the large gear is 4.5 inches?