Consider this problem:
A simple coupling for connecting two axes in a motor consists of two cylindrical plates (r = 0.6 m) that can be pressed together if necessary. Plate A with mass mA = 6 kg is accelerated in 2 s to an angular velocity of ω1 = 7.2 rad / s. Clutch disc B with mB = 9 kg is still at rest. If the plates are now coupled together, they both rotate with a reduced angular velocity ω2.
What is the value of the angular momentum and torque of plate A before the coupling took place? Which angular velocity ω2 is reached after coupling?
Now I had no problem calculating the angular moment and torque of plate A before the coupling.Should be
$$ L_a = 7,776 kgm^2/s $$ $$ M_a = 3,888 Nm $$
Now for the angular velocity after the coupling I though of that this way. We have the plate A with La angular momentum, and plate B with Lb angular momentum.Since Lb = 0 because the plate is standing still we can take our angular momentum just to be La. For the moment of inertia we have to take into account that the total weight has changed,from 6 to 15kg. So I calculated Itotal and got $$ I_t = 2,7 kgm^2 $$ And now we can easily calcualte the angular velocity $$ \omega = 2,88 rad/s $$.
Now what is bugging me is the fact that I have simply assumed that the angular momentum stays the same after coupling.Since angular momentum is dependent on the moment of inertia and angular velocity I am not sure if I can make this assumption. If plate B was also moving how would I calculate the angular momentum than? Would simply adding them do the trick?