Deeper Rotational Budget Scans

Inertia Mass Radius-Square Three-Row Scan

Moment of inertia changes linearly with mass and quadratically with radius. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One-meter radius gives two inertia units

Mass 2 kg at radius 1 m gives inertia 2 kilogram meter squared.

I=2×12=2I=2\times1^2=2
Inertia mass radius rowOne point mass makes inertia m times r squared.r=1 mm=2 kgr=1 mI=2 kg*m^2

Doubling radius quadruples inertia

Mass 2 kg at radius 2 m gives inertia 8 kilogram meter squared.

I=2×22=8I=2\times2^2=8
Inertia mass radius rowOne point mass makes inertia m times r squared.r=2 mm=2 kgr=2 mI=8 kg*m^2

Doubling mass doubles the already-squared row

Mass 4 kg at radius 2 m gives inertia 16 kilogram meter squared.

I=4×22=16I=4\times2^2=16
Inertia mass radius rowOne point mass makes inertia m times r squared.r=2 mm=4 kgr=2 mI=16 kg*m^2