Calculate RPM Ratio for Sprockets

What is the relationship between the number of teeth on a sprocket and its speed in a gear system?

Answer:

In a gear system, the speed of rotation (RPM) is inversely proportional to the number of teeth. If a 50-tooth sprocket turns at 20 RPM, a 30-tooth sprocket in the same system will turn faster, approximately at 33.33 RPM.

Explanation:

In a gear system, the speed of rotation, or RPM (revolutions per minute), is inversely proportional to the number of teeth. This is an example of the conservation of angular momentum.

If a 50-tooth sprocket turns at 20 RPM, a 30-tooth sprocket on the same system will turn faster, due to the smaller number of teeth. To find the speed of the 30-tooth sprocket, you can use the formula: (RPM of 50-tooth sprocket x Number of teeth on 50-tooth sprocket) / Number of teeth on 30-tooth sprocket. So, (20 RPM x 50 Teeth) / 30 Teeth = 33.33 RPM. Hence, the 30-tooth sprocket will turn at an approximate speed of 33.33 RPM.