Explanation:
ω = ω₀ + αt
θ = ω₀ t + ½ αt²
We need to eliminate t from the system of equations. Solve for t in the first equation, then substitute it into the second equation.
t = (ω − ω₀) / α
θ = ω₀ (ω − ω₀) / α + ½ α ((ω − ω₀) / α)²
θ = ω₀ (ω − ω₀) / α + ½ (ω − ω₀)² / α
αθ = ω₀ (ω − ω₀) + ½ (ω − ω₀)²
αθ = ω₀ω − ω₀² + ½ (ω² − 2ω₀ω + ω₀²)
αθ = ω₀ω − ω₀² + ½ ω² − ω₀ω + ½ ω₀²
αθ = ½ ω² − ½ ω₀²
2αθ = ω² − ω₀²