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

Equivalent Polar Moment Of Inertia Geared System

Two gears A and B with polar moments of inertia I_A and I_B are mounted on shafts and roll without slip. Given the radii ratio n = R_A/R_B, derive the equivalent polar moment of inertia seen at gear A by writing the equations of motion at both gears and applying the geometric constraint relating their angular accelerations.

✓ All 3 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":1,"n":1}	2	2	✓
2	{"I_A":2,"I_B":3,"n":2}	14	14	✓
3	{"I_A":5,"I_B":2,"n":3}	23	23	✓

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Endpoint

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

Inputs (3)

I_Anumberdefault 1
I_Bnumberdefault 1
nnumberdefault 2

Example

curl -sX POST http://localhost:3001/api/calculators/engineering-optimzation/equivalent-polar-moment-of-inertia-geared-system/compute \
  -H "Content-Type: application/json" \
  -d '{"inputs":{"I_A":1,"I_B":1,"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-of-inertia-geared-system computation; problem text paraphrased.

AI disclosure: Calculator code generated by anthropic/claude-haiku-4-5-20251001; verified by 3 test cases.