Concepts Of Physics MCQ Edition [Volume 1]PhysicsRotational Mechanics
A wheel with a moment of inertia of 0.10 kg-m ^2 rotates about a shaft at an angular speed of 160 rev/minute . A second wheel is set into rotation at 300 rev/minute and is then coupled to the same shaft, causing both wheels to finally rotate at a common angular speed of 200 rev/minute . Determine the moment of inertia of the second wheel.
Options
- A0.05 kg-m ^2
- B0.04 kg-m ^2
- C0.36 kg-m ^2
- D0.08 kg-m ^2
Correct answer
B. 0.04 kg-m ^2
Step-by-step solution
By conservation of angular momentum: I₁ ₁ + I₂ ₂ = (I₁ + I₂) Given I₁ = 0.10 kg-m ^2 , ₁ = 160 rev/minute , ₂ = 300 rev/minute , and = 200 rev/minute . Substituting the values: 0.10 160 + I₂ 300 = (0.10 + I₂) 200 16 + 300 I₂ = 20 + 200 I₂ 100 I₂ = 4 I₂ = 0.04 kg-m ^2