A clutch consists of two disks with rotational inertias I1 = 4 kg∙m2 and I2 = 2 kg∙m2
which are mounted to rotate about a common axis. Disk 1 is initially rotating at 60
rpm and disk 2 is initially at rest. The two disks are then pressed together so that, after some slippage, they both rotate at the same angular speed. (a) What is their final angular speed? (b) How much kinetic energy, if any, was lost when the disks were engaged?

Question

A clutch consists of two disks with rotational inertias I1 = 4 kg∙m2 and I2 = 2 kg∙m2
which are mounted to rotate about a common axis. Disk 1 is initially rotating at 60
rpm and disk 2 is initially at rest. The two disks are then pressed together so that, after some slippage, they both rotate at the same angular speed. (a) What is their final angular speed? (b) How much kinetic energy, if any, was lost when the disks were engaged?

anonymous · Answer

I have the answers. I just want to know the formulas to get to the answers.

anonymous · Answer

Conserve angular momentum as there is no net external force which has a tendency to produce torque.
L(initial)=L(final)
$$I1 \omega 1+ I2 \omega 2=(I1+I2) \omega'$$
then calculate angular frequency omega dashed
the momentum is conserved between two points one when the disks are rotating independently and other when they are rotating together.

anonymous · Answer

So KE lost is?

anonymous · Answer

Sarkar? Ke lost is KEfinal - KE initial... but what is the final inertia? of the two objects ?