What is the speed in rpm of the second gear driven by a 330 mm diameter gear revolving at 200 rpm and driving a 150 mm diameter gear?

To determine the speed of the second gear, we can use the relationship between the diameters of the gears and their speeds. When two gears are meshed together, the speed and size of the gears follow the principle that the product of the speed (in rpm) and the diameter of the gear remains constant.

Given:

• The first gear has a diameter of 330 mm and rotates at 200 rpm.

• The second gear has a diameter of 150 mm.

First, we find the relationship between the speeds of the two gears using the formula:

[

\text{Speed}_1 \times \text{Diameter}_1 = \text{Speed}_2 \times \text{Diameter}_2

]

Substituting the known values:

[

200 , \text{rpm} \times 330 , \text{mm} = \text{Speed}_2 \times 150 , \text{mm}

]

Next, we solve for the speed of the second gear:

[

\text{Speed}_2 = \frac{200 \times 330}{150}

]

Calculating the values:

[

\text{Speed}_2 = \frac{66000}{150} =