Rotational Relation Cross Scans

Angular Momentum Compensation Three-Row Scan

inertia trades against spin

The same angular momentum can pair high inertia with low spin. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

High inertia needs low spin for the same L

Inertia 12 times spin rate 2 gives the same angular momentum 24.

L=12×2=24L=12\times2=24
Angular momentumInertia times spin rate sets L.r=2 mm=3 kgr=2 mI=12 kg*m^2omega=2 1/sL=24 kg*m^2/s

Middle inertia doubles the spin

Inertia 6 times spin rate 4 gives the same angular momentum 24.

L=6×4=24L=6\times4=24
Angular momentumInertia times spin rate sets L.r=1 mm=6 kgr=1 mI=6 kg*m^2omega=4 1/sL=24 kg*m^2/s

Small inertia needs the fastest spin

Inertia 3 times spin rate 8 gives the same angular momentum 24.

L=3×8=24L=3\times8=24
Angular momentumInertia times spin rate sets L.r=1 mm=3 kgr=1 mI=3 kg*m^2omega=8 1/sL=24 kg*m^2/s