Question Detail
Question
A wheel is rotating freely at angular speed of 800 rev/min on a shaft whose rotational inertia is negligible. A second wheel is initially at rest and with twice the rotational inertia of the first is suddenly coupled on a shaft. What is the angular speed of the resultant shaft and the two wheels?
Correct Answer
Option D is the correct answer.
Detailed Explanation
Apply conservation of angular momentum: I₁ω₁ = (I₁ + I₂)ω_f. Given I₂ = 2I₁, so I₁ × 800 = (I₁ + 2I₁) × ω_f = 3I₁ × ω_f. Therefore, ω_f = 800 / 3 ≈ 267 rev/min.
Hint
Angular momentum is conserved. The final moment of inertia is the sum of both wheels.