Question

Part a how many inches would a point on the outer edge of the large gear travel in a 150º rotation?

Answer 1

Approximately 20.47 inches

How to calculate the value?

given large central gear radius r = 4 inches.

small central gear radius = 2 inches.

if large gear travel in a 150º rotation distance travelled by large gear is

$\frac{150 {}^{0} }{360 {}^{0} } \times 2 \times \pi \times 4 \\ \frac{10}{3} \times \pi \\ 10.47 \: inches$

so, distance travelled by outer edge is 10.47 inches.

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Disclaimer : This question was incomplete in potal.Here is the complete question

Question: 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 the 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 150º rotation?