Discussion
A motor of inertia 0.5 kg·m² drives through a 5:1 reduction a load of inertia 20 kg·m². The total inertia referred to the motor shaft is
Answer: A
Correct answer: 1.3 kg·m²
The load inertia refers through the square of the ratio and is then added to the motor’s own:
\[ J_{total} = 0.5 + \frac{20}{5^2} = 0.5 + 0.8 = 1.3 \ \mathrm{kg\,m^2} \]The 20.5 answer adds the load inertia unreferred, which would make the drive sixteen times harder to accelerate than it is. The square law is what makes gearing so effective at taming a large slow-moving inertia.
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