Problem:
The number of teeth in three meshed circular gears A,B,C are x,y,z, respectively. The angular speeds, in revolutions per minute, of A,B,C are in the proportion
Answer Choices:
A. x:y:z
B. z:y:x
C. y:z:x
D. yz:xz:xy
E. xz:yx:zy
Solution:
Since the teeth are all the same size, equally spaci3l and are meshied, they all move with the same absolute speed v(ν is the distance a point on the circumference moves per unit of time). Let α,β,γ be the angular speeds of A,B,C, respectively. If a,b,c represent the lengths of the circumferences of A,B,C, respectively, then
α=av​,β=bv​,γ=cv​
Therefore, αa=βb=γc or, equivalently,
a1​α​=b1​β​=c1​γ​.
Thus the angular speeds are in the proportion
a1​:b1​:c1​
Since a,b,c, are proportional to x,y,z, respectively, the angular speeds are in the proportion
x1​:y1​:z1​
Multiplying each term by xyz gives the proportion
yz:xz:xy.
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