What is the required number of teeth for a gear that turns at 200 rpm when in mesh with an 80 tooth gear turning at 500 rpm?

To determine the required number of teeth for the gear that turns at 200 rpm when in mesh with an 80-tooth gear turning at 500 rpm, you can use the relationship between the gears based on their speeds and the number of teeth.

The fundamental principle is that the product of the gear's speed (in rpm) and the number of teeth must be equal for both gears since they are in mesh. This can be expressed in the equation:

Speed_1 × Teeth_1 = Speed_2 × Teeth_2

Substituting the known values into the equation:

500 rpm × 80 teeth = 200 rpm × Teeth_2

Now you can solve for Teeth_2:

40,000 = 200 × Teeth_2

To find Teeth_2, divide both sides by 200:

Teeth_2 = 40,000 / 200

Teeth_2 = 200

This calculation shows that the gear that turns at 200 rpm must have 200 teeth to maintain the relationship of speed and teeth with the 80-tooth gear turning at 500 rpm. This understanding of rotational dynamics and the gear ratio is essential for successful millwright practices.