How many teeth does the second gear have if the first gear rotates at 60 rpm with 23 teeth and the second gear rotates at 5 rpm?

To determine the number of teeth on the second gear, we can use the relationship between the number of teeth and the rotational speed of gears. The principle at work here is that the product of the number of teeth and the rotational speed (rpm) must remain constant for two meshed gears.

Given that the first gear has 23 teeth and rotates at 60 rpm, we can calculate the relationship for the second gear, which rotates at 5 rpm.

We can set up the equation as follows:

(Number of teeth on first gear) × (Speed of first gear) = (Number of teeth on second gear) × (Speed of second gear)

Substituting the known values into the equation gives us:

23 teeth × 60 rpm = Number of teeth on second gear × 5 rpm

Calculating the left side:

23 teeth × 60 rpm = 1380

So, we have:

1380 = (Number of teeth on second gear) × 5 rpm

Next, we can solve for the number of teeth on the second gear:

Number of teeth on second gear = 1380 / 5

Number of teeth on second gear = 276 teeth

Thus, the correct answer is that the second gear has