A 30 -tooth gear on a motor shaft drives a larger gear having 66 teeth. If the motor shaft rotates at 1100 rpm , what is the speed of the larger gear?

To find the speed of the larger gear, you can use the gear ratio formula, which is based on the number of teeth. The gear ratio (GR) can be calculated as the number of teeth on the driven gear (larger gear) divided by the number of teeth on the driving gear (smaller gear): GR = Teeth on larger gear / Teeth on smaller gear = 66 / 30 = 2.2. Then, the speed of the larger gear (N₂) can be calculated using the formula: N₂ = N₁ / GR, where N₁ is the speed of the motor shaft. So, N₂ = 1100 rpm / 2.2 ≈ 500 rpm. The larger gear rotates at approximately 500 rpm. Gear systems are fascinating because they’re all around us, from bicycles to car transmissions! The idea of using different sized gears to reduce or increase speed and torque dates back centuries, showcasing human ingenuity in mechanics. Just imagine the ancient craftsmen figuring out how to put gears together to create new technologies that changed the world! When working with gear ratios, a common mistake is forgetting to simplify the ratio completely or miscalculating the teeth counts. It’s vital to check that the teeth numbers used for each gear are accurate. Additionally, keep in mind the effect of gear ratios on torque; larger gears can provide more torque at a lower speed, so always consider what you need for your specific application!