Question

Solve this gear problem.

Gear 1 = 30 teeth
Speed, gear 1 = 150 r.p.m.
Speed, gear 2 = 50 r.p.m.
Teeth, gear 2 = ?

Answer 1

Hello!

The answer is:

The number of teeth of Gear 2 is 90 teeth.

`N_(2)=90teeth`

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.

`N_(1)Z_(1)=N_(2)Z_(2)`

Where,

N, are the rpm of the gears

Z, are the teeth of the gears.

We are given the following information:

`Z_(1)=30teeth\\N_(1)=150RPM\\N_(2)=50RPM`

Then, substituting and calculating we have:

`N_(1)Z_(1)=N_(2)Z_(2)`

`150RPM*30teeth=N_(2)50RPM`

`N_(2)=(150RPM*30teeth)/(50RPM)=90teeth`

`N_(2)=90teeth`

Hence, we have that the number of teeth of Gear 2 is 90 teeth.

Have a nice day!