Explanation:
Angular impulse = change in angular momentum
Mg Δt = ΔHg
Mg Δt = Hg₂ − Hg₁
Rearranging, initial angular momentum + angular impulse = final angular momentum
Hg₁ + Mg Δt = Hg₂
Initially, the rocket is not turning, so ω₁ = 0 rad/s.
Hg₁ = I ω₁
Hg₁ = (900 kg m²) (0 rad/s)
Hg₁ = 0 kg m²/s
The total moment applied is the sum of the perpendicular components of each force multiplied by the distance. Take counterclockwise to be positive.
Mg = (400 N cos 15° × 1.5 m) + (400 N cos 15° × 1.5 m)
Mg = 2 (400 N cos 15° × 1.5 m)
The time of the impulse Δt is 0.3 s.
The final angular momentum is the product of the moment of inertia and the final angular velocity.
Hg₂ = I ω₂
Hg₂ = (900 kg m²) ω₂
Plugging everything in:
0 kg m²/s + 2 (400 N cos 15° × 1.5 m) (0.3 s) = (900 kg m²) ω₂
ω₂ = 0.386 rad/s
