Is the acceleration of smaller gears always 4 times greater in a 4:1 gear ratio?

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In a 4:1 gear ratio, the smaller gear indeed accelerates four times faster than the larger gear. This relationship holds true for angular velocities, angular displacements, and angular accelerations, meaning they all adhere to the same ratio. The acceleration of both gears is interconnected, as they accelerate in sync according to the defined gear ratio. Therefore, the acceleration of the smaller gear is consistently four times greater than that of the larger gear. Understanding this relationship is crucial for analyzing gear systems effectively.
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Say we have a gearing system of the ratio 4:1 is the acceleration of the smaller gear 4 times greater than the acceleration of the larger gear or do they both accelerate in the same way or is it a completely different more complex relationship? Thank you in advance for any help.
 
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I believe the definition is that the gear ratio is the ratio of the angular velocities of both gears (input over output). So the angular velocity of the input is 4 times that of the output in your example and since they would accelerate in step, I believe the ratio would apply to angular accelerations as well.
 
grindfreak is correct; the gear ratio gives the ratio of angular displacements, or angular velocities, or angular accelerations, however you want to look at it.
 

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