Hello!
The answer is:
The number of teeth of Gear 2 is 90 teeth.
[tex]N_{2}=90teeth[/tex]
Why?
To calculate the number of teeth for the Gear 2, we need to use the following formula that establishes a relation between the number of RPM and the number of teeth of two or more gears.
[tex]N_{1}Z_{1}=N_{2}Z_{2}[/tex]
Where,
N, are the rpm of the gears
Z, are the teeth of the gears.
We are given the following information:
[tex]Z_{1}=30teeth\\N_{1}=150RPM\\N_{2}=50RPM[/tex]
Then, substituting and calculating we have:
[tex]N_{1}Z_{1}=N_{2}Z_{2}[/tex]
[tex]150RPM*30teeth=N_{2}50RPM[/tex]
[tex]N_{2}=\frac{150RPM*30teeth}{50RPM}=90teeth[/tex]
[tex]N_{2}=90teeth[/tex]
Hence, we have that the number of teeth of Gear 2 is 90 teeth.
Have a nice day!
