Question

question 6
2 pts
what is the speed of a gear with 42 teeth driven by another gear with 14 teeth during at 420 rpm? _____ rpm

Explanation:

Step1: Set up the gear - ratio formula

The ratio of the number of teeth of two gears is inversely proportional to their rotational speeds. Let $N_1$ be the number of teeth of the driving gear, $N_2$ be the number of teeth of the driven gear, $R_1$ be the rotational speed of the driving gear, and $R_2$ be the rotational speed of the driven gear. The formula is $N_1\times R_1 = N_2\times R_2$.

Step2: Substitute the given values

We know that $N_1 = 14$, $R_1=420$ RPM, and $N_2 = 42$. Substituting these values into the formula $14\times420=42\times R_2$.

Step3: Solve for $R_2$

First, calculate $14\times420 = 5880$. Then, we have the equation $5880 = 42\times R_2$. To find $R_2$, divide both sides of the equation by 42: $R_2=\frac{5880}{42}=140$ RPM.

Answer:

140