SOLUTION: Two gears are adjusted so that the smaller gear with radius of 2.5 cm drives the larger one with radius of 4.8 cm. If the smaller gear rotates through an angle of 5π/4 radians

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Question 797183: Two gears are adjusted so that the smaller gear with radius of 2.5 cm drives the larger one with radius of 4.8 cm. If the smaller gear rotates through an angle of 5π/4 radians, through what angle measurement in degrees will the larger gear rotate?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The measure of an angle in radians is the arc divided by the radius:
angle=arc%2Fradius <---> angle%2Aradius=arc
As the small gear rotates through an angle of 5pi%2F4 radians, the point that was originally in contact with the other gear moves a distance of
%285pi%2F4%29%2A%282.5cm%29 along the circumference of the small gear.

In the large gear, the point that was originally in contact with the other gear moves the same distance along the circumference of the small gear.
If that distance correspond to an angle measuring x radians, that distance is
x%2A%284.8cm%29.
So, x%2A%284.8cm%29=%285pi%2F4%29%2A%282.5cm%29-->x=%285pi%2F4%29%2A%282.5cm%2F%224.8+cm%22%29-->x=%285%2F4%29%2825%2F48%29pi-->x=125pi%2F192
That's 70.3125%5Eo.
The points of the gears that were in contact end up at A and B after that turn.