Question

A cylinder of mass 250 kg and radius 2.60 m is rotating at 4.00 rad/s on a frictionless.

Two more identical nonrotating cylinders fall on top of the first. Because of friction
between the cylinders they will eventually all come to rotate at the same rate. What is this final angular velocity?​

Answer 1

The angular momentum of a cylinder, when it is rotating with constant angular velocity is Lini =Iωi

. When two cylinders are added to the rotating cylinder, which are identical in their dimensions, the moment of inertia of the entire system increases (since mass increases). The final moment of inertia will be 3I

Since friction exist, all the cylinders start rotating with same angular velocity, the new angular velocity can be calculated using conservation of angular momentum

Thus, Iωi =3Iωf ⟹ωf =ωi/3 = 0.33ωi