Rotational Relation Cross Scans

Rotational Energy Omega-Square Three-Row Scan

spin is squared

Fixed inertia makes rotational energy grow with spin squared. 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 spin unit gives four joules

With inertia fixed at 8, spin 1 gives rotational energy 4 joules.

Krot=1/2×8×12=4K_{\mathrm{rot}}=1/2\times8\times1^2=4
Rotational energyRotational kinetic energy has a half factor.r=2 mm=2 kgr=2 mI=8 kg*m^2omega=1 1/sKrot=4 J

Doubling spin quadruples energy

With inertia fixed at 8, spin 2 gives rotational energy 16 joules.

Krot=1/2×8×22=16K_{\mathrm{rot}}=1/2\times8\times2^2=16
Rotational energyRotational kinetic energy has a half factor.r=2 mm=2 kgr=2 mI=8 kg*m^2omega=2 1/sKrot=16 J

Tripling spin gives nine times the first energy

With inertia fixed at 8, spin 3 gives rotational energy 36 joules.

Krot=1/2×8×32=36K_{\mathrm{rot}}=1/2\times8\times3^2=36
Rotational energyRotational kinetic energy has a half factor.r=2 mm=2 kgr=2 mI=8 kg*m^2omega=3 1/sKrot=36 J