For spur gears, if gear 1 has N1 teeth and gear 2 has N2 teeth, the speed ratio ω1/ω2 equals?

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Multiple Choice

For spur gears, if gear 1 has N1 teeth and gear 2 has N2 teeth, the speed ratio ω1/ω2 equals?

Explanation:
The speeds of two meshing spur gears are linked by the fact that the tangential velocity at the point where they contact must be the same on both gears. This gives the relation ω1 R1 = ω2 R2. The pitch radii R1 and R2 scale with the number of teeth, so R ∝ N, and thus R2/R1 = N2/N1. Rearranging the tangential-velocity equality yields the speed ratio ω1/ω2 = N2/N1. Therefore the correct relationship is the driven gear turning slower in proportion to its larger tooth count, or faster if it has fewer teeth. The other forms don’t come from the equal-tangential-velocity condition and thus don’t represent the actual gear motion.

The speeds of two meshing spur gears are linked by the fact that the tangential velocity at the point where they contact must be the same on both gears. This gives the relation ω1 R1 = ω2 R2. The pitch radii R1 and R2 scale with the number of teeth, so R ∝ N, and thus R2/R1 = N2/N1. Rearranging the tangential-velocity equality yields the speed ratio ω1/ω2 = N2/N1. Therefore the correct relationship is the driven gear turning slower in proportion to its larger tooth count, or faster if it has fewer teeth. The other forms don’t come from the equal-tangential-velocity condition and thus don’t represent the actual gear motion.

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