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Mass Properties (MOI & CG)

Mass moment of inertia sets how hard something is to accelerate rotationally — the key input to motor sizing. Use the parallel-axis theorem to shift an inertia off its own centroid, and a mass-weighted average to find a composite CG.

Shape

Mass (kg)

Dim 1 — radius or length (m)

Dim 2 — inner r / side b (m)

Axis offset for parallel axis (m)

Moment of inertia

—

Shifted (parallel axis)

—

Radius of gyration

—

Dim 2 is only used by the hollow-cylinder (inner radius) and prism (second side) cases. Reflected inertia through a gearbox divides by the ratio squared.

A helper, not a substitute for engineering judgment. Verify against the governing standard.