What is the speed of the second gear if a gear wheel 65 cm in diameter revolves at 225 r/min and drives a wheel 85 cm in diameter?

To determine the speed of the second gear, we can use the relationship between the diameters of the gears and their rotational speeds. The key principle is that the product of the speed and diameter remains constant when two gears are meshed together.

First, we need to convert the diameters of the gears into a useful formula. The formula linking the speed of rotation of the first gear (which is 65 cm in diameter, revolving at 225 r/min) and the second gear (which is 85 cm in diameter) is:

[

\text{Speed of Gear 1} \times \text{Diameter of Gear 1} = \text{Speed of Gear 2} \times \text{Diameter of Gear 2}

]

Substituting the values we know:

[

225 , \text{r/min} \times 65 , \text{cm} = \text{Speed of Gear 2} \times 85 , \text{cm}

]

Next, we calculate the left side:

[

225 \times 65 = 14625

]

Now, we can set up the equation to solve for the speed of the second gear:

[

14625 =