Question

A 12​-tooth gear on a motor shaft drives a larger gear having 42 teeth. If the motor shaft rotates at 700 ​rpm, what is the speed of the larger​ gear? The speed of the larger gear is nothing rpm.

Answer 1

203 rpm

Explanation:

The speed of the larger gear can be calculated using the following equation:

`v = \omega*R`

Where:

ω: is the angular velocity of the motor = 700 rpm

R: is the gear ratio

The gear ratio is the following:

`R = (n_((a)))/(n_((b)))`

Where:

n(a): is the number of teeth on the small gear = 12 teeth

n(b): is the number of teeth on the larger gear = 42 teeth

The gear ratio is:

`R = (12)/(42) = 0.29`

Now, the speed of the larger gear is:

`v = \omega*R = 700 rpm*0.29 = 203 rpm`

Therefore, the speed of the larger gear is 203 rpm.

I hope it helps you!