A boy stands on a platform that can freely rotate about its vertical axis. He is holding an open umbrella, with the umbrella's axis coinciding with that of the platform. The moment of inertia for the "platform plus boy" system is 3.0 10⁻³ kg-m ^2 , and for the umbrella it is 2.0 10⁻³ kg-m ^2 . The boy then begins to spin the umbrella about the axis at an angular speed of 2.0 rev/s relative to himself. Calculate the a

Step-by-step solution

Let I₁ be the moment of inertia of the platform plus boy, and I₂ be the moment of inertia of the umbrella. I₁ = 3.0 10⁻³ kg-m ^2 I₂ = 2.0 10⁻³ kg-m ^2 Let ₁ be the angular velocity of the platform relative to the ground. The angular velocity of the umbrella relative to the platform is _ rel = 2.0 rev/s . The angular velocity of the umbrella relative to the ground is ₂ = ₁ + _ rel . Since no external torque acts on the system about the vertical axis, the total angular momentum is conserved. L_i = L_f 0 = I₁ ₁ + I₂ ₂