Deeper Rotational Budget Scans

Inertia Mass Radius-Square Three-Row Scan

Moment of inertia changes linearly with mass and quadratically with radius.

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