How do you calculate the speed of a larger gear if a smaller gear with 13 teeth drives it at 550 RPM and has 63 teeth?

To calculate the speed of the larger gear, you can use the formula that relates the speeds and number of teeth on the gears. This formula is based on the principle that the product of the speed (RPM) and the number of teeth for both gears remains constant:

( \text{Speed}{\text{small}} \times \text{Teeth}{\text{small}} = \text{Speed}{\text{large}} \times \text{Teeth}{\text{large}} )

In this situation, the small gear has 13 teeth and rotates at 550 RPM, while the larger gear has 63 teeth. Plugging these values into the formula provides:

( 550 , \text{RPM} \times 13 , \text{teeth} = \text{Speed}_{\text{large}} \times 63 , \text{teeth} )

Calculating the left side gives:

( 7150 = \text{Speed}_{\text{large}} \times 63 )

Now, to find the speed of the larger gear, you can rearrange the equation:

( \text{Speed}_{\text{large}} = \frac{7150}{