Rot KE = \frac{1}{2}Iω^{2}

Rot KE_{f} = Rot KE_{i} + Work_{net}
Rot KE_{f} = Rot KE_{i} + ∫ τ⃗_{net} · d⃗θ

|τ| = |r| |F | sin(θ)

r⃗ = r_{x} î + r_{y} ĵ + r_{z} k̂

F⃗ = F_{x} î + F_{y} ĵ + F_{z} k̂

r⃗ = 3 m î + 0 mĵ − 5 m k̂

F⃗ = 6 N î + 2 N ĵ + 0 Nk̂

5 × 3 = 15

\begin{aligned}A⃗ & = 5î + 8ĵ \\ B⃗ & = 1î − 3ĵ \end{aligned}

|A × B| = |A| |B| sin(θ)

\begin{aligned}A⃗ & = 5î + 8ĵ + 0k̂ \\ B⃗ & = 1î − 3ĵ + 0k̂ \end{aligned}

\begin{aligned}A × B & = [(8)(0) − (0)(−3)] î − [(0)(5) − (1)(0)] ĵ + [(5)(−3) − (8)(1)] k̂ \\ & = 0î + 0ĵ − 23k̂ \end{aligned}

\begin{aligned}A⃗ & = 1î + 2ĵ + 3k̂ \\ B⃗ & = 3î + 2ĵ + 1k̂ \end{aligned}