Question

in the gear train shown in the illustration, if the driver gear rotates at 120 revolutions per minute (rpm), at what rpm does the driven gear rotate? a 40 b 60 c 120 d 360

Explanation:

Step1: Use the gear ratio formula

The formula for gear rotation is \(N_1\times T_1 = N_2\times T_2\), where \(N_1\) is the speed of the driver gear, \(T_1\) is the number of teeth on the driver gear, \(N_2\) is the speed of the driven gear, and \(T_2\) is the number of teeth on the driven gear.
We are given \(N_1 = 120\) rpm, \(T_1=12\), and \(T_2 = 36\).

Step2: Solve for \(N_2\)

Substitute the values into the formula: \(120\times12=N_2\times36\).
First, calculate \(120\times12 = 1440\). Then, \(N_2=\frac{1440}{36}\).
\(N_2 = 40\)

Answer:

A. 40