Question

A solid disk of mass m1 = 9.5 kg and radius r = 0.19 m is rotating with a constant angular velocity of ω = 39 rad/s. a thin rectangular rod with mass m2 = 3.3 kg and length l = 2r = 0.38 m begins at rest above the disk and is dropped on the disk where it begins to spin with the disk. 1) what is the initial angular momentum of the rod and disk system?

Answer 1

In order to solve the equation, you must find first the following:
Solid disk = ½*m1*R² = ½ * 9.5kg * (0.25m)² = 0.296875 kg·m² I_rod = m2*L²/12 = 3.3kg * (0.38m)² / 12 = 0.03971 kg·m²
the initial angular momentum is computed by:L = solid disk * ω = 0.296875kg·m² * 39rad/s= 11.578125 kg·m²/s