Question 1096677: Finding the angular speed:
The centers of two meshed gears are 21 in. apart. If the smaller one moves through 3 radians per sec. and has a radius of 9 in., what is the angular speed of the larger?
Please help me :(
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! The centers of two meshed gears are 21 in. apart. If the smaller one moves through 3 radians per sec. and has a radius of 9 in., what is the angular speed of the larger?
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Step 1, find the 2nd radius.
21 - 9 = 12 inches.
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It's 4/3 the smaller radius --> 3/4 the angular speed.
--> 2.25 rad/sec
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! The distance between the centers is the sum of the radii, So, the radius of the larger gear is
21 inches - 9 inches = 12 inches.
The angle in radians is the length of the arc divided by the radius,
so the length of the arc is the radius times the measure of the angle in radians.
During 1 second, the smaller gear turns 3 radians,
meaning that the point of contact with the larger gear moves along an arc of length
 on the edge of the small gear.
For the large gear, unless the gears are slipping, the point of contract .must have moved the same distance.
However, it moved along an arc of a circle of radius = 12 inches.
The measure of the angle in radians is
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