Two gears

The two gears fit together. The larger gear has 32 teeth, the smaller has 20 teeth less. How many times does turn a smaller gear if the bigger gear turns three times?

Result

n2 =  8

Solution:

z1=32 z2=z120=3220=12  n1=3  s1=s2 n2 z2=n1 z1 n2=n1 z1z2=3 3212=8z_{1}=32 \ \\ z_{2}=z_{1}- 20=32- 20=12 \ \\ \ \\ n_{1}=3 \ \\ \ \\ s_{1}=s_{2} \ \\ n_{2} \cdot \ z_{2}=n_{1} \cdot \ z_{1} \ \\ n_{2}=n_{1} \cdot \ \dfrac{ z_{1} }{ z_{2} }=3 \cdot \ \dfrac{ 32 }{ 12 }=8



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