Question Detail
Question
A flywheel requires 2 s to rotate through 234 radians. Its angular velocity at the end of this time is 108 rad/s. Find the constant angular acceleration.
Correct Answer
Option A is the correct answer.
Detailed Explanation
Using θ = ω_avg × t, ω_avg = (ω₀ + ω)/2. So 234 = ((ω₀ + 108)/2) × 2 = ω₀ + 108 → ω₀ = 234 - 108 = 126 rad/s. Then α = (ω - ω₀)/t = (108 - 126)/2 = -18/2 = -9 rad/s². Not matching. Using θ = ω₀t + ½αt²: 234 = ω₀×2 + ½α×4 = 2ω₀ + 2α. Also ω = ω₀ + αt → 108 = ω₀ + 2α → ω₀ = 108 - 2α. Substitute: 234 = 2(108 - 2α) + 2α = 216 - 4α + 2α = 216 - 2α → 2α = 216 - 234 = -18 → α = -9 rad/s². Still -9. Options are positive, maybe they want magnitude 9 rad/s², not in options. If they used θ = (ω₀ + ω)t/2 = (126+108)×2/2 = 234, correct. α = -9. Option A is 20, not matching.
Hint
Use rotational kinematics equations.