Engineering optimzation·equivalent-polar-moment-inertia-geared-system

Equivalent Polar Moment Inertia Geared System

Two gears A and B with individual polar moments of inertia I_A and I_B are in contact with radii ratio n = R_A/R_B. Using the equations of motion and geometric constraints from the gear contact, derive the equivalent polar moment of inertia as seen from gear A.

✓ All 2 test cases pass.

Inputs

Polar moment of inertia of gear A

Rotational inertia of gear A

Polar moment of inertia of gear B

Rotational inertia of gear B

Radii ratio

Ratio R_A / R_B of gear radii

Test cases

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#	Inputs	Expected	Got	Status
1	{"I_A":1,"I_B":0.5,"n":2}	3	3	✓
2	{"I_A":2,"I_B":1,"n":1}	3	3	✓

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Endpoint

POST/api/calculators/engineering-optimzation/equivalent-polar-moment-inertia-geared-system/compute

Inputs (3)

I_Anumberdefault 1
I_Bnumberdefault 0.5
nnumberdefault 2

Example

curl -sX POST http://localhost:3001/api/calculators/engineering-optimzation/equivalent-polar-moment-inertia-geared-system/compute \
  -H "Content-Type: application/json" \
  -d '{"inputs":{"I_A":1,"I_B":0.5,"n":2}}'

Try it live

Edit the body below, then click Call API.

Request body

Response

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Source: Pattern from: Ch1.pdf. Reproduces a standard equivalent-polar-moment-inertia-geared-system computation; problem text paraphrased.

AI disclosure: Calculator code generated by anthropic/claude-haiku-4-5-20251001; verified by 2 test cases.