In a simple gear train, the gear ratio is the inverse of the speed ratio.

In a simple gear train, the gear ratio is the inverse of the speed ratio.

• A. True
• B. False
• C. Only for certain configurations
• D. It depends on the motor type

Answer: (B)

Think about how meshed gears relate speeds to their tooth counts. The tangential speed at the pitch circles must be the same, so ω1 r1 = ω2 r2. Since the pitch radius is proportional to the number of teeth, r ∝ N, which gives ω1/ω2 = N2/N1, or equivalently ω2/ω1 = N1/N2. The gear ratio is typically defined as the driver teeth over the driven teeth, N1/N2. That means the gear ratio equals the speed ratio (output speed divided by input speed) in magnitude, not its inverse. The statement is false because the two quantities have the same value when defined consistently. For example, a driver with 20 teeth and a driven with 40 teeth yields ω2/ω1 = 0.5 and gear ratio N1/N2 = 0.5; they match in magnitude (the direction reverses due to meshing, but the magnitudes align).

Think about how meshed gears relate speeds to their tooth counts. The tangential speed at the pitch circles must be the same, so ω1 r1 = ω2 r2. Since the pitch radius is proportional to the number of teeth, r ∝ N, which gives ω1/ω2 = N2/N1, or equivalently ω2/ω1 = N1/N2.

The gear ratio is typically defined as the driver teeth over the driven teeth, N1/N2. That means the gear ratio equals the speed ratio (output speed divided by input speed) in magnitude, not its inverse. The statement is false because the two quantities have the same value when defined consistently. For example, a driver with 20 teeth and a driven with 40 teeth yields ω2/ω1 = 0.5 and gear ratio N1/N2 = 0.5; they match in magnitude (the direction reverses due to meshing, but the magnitudes align).