I could? Do I need to know ##w## to do this? Because I tried to use them, but ended up replacing ##Iw## by ##I\frac{v}{CM}##, where ##CM## is the distance from the pivot to the center of the mass of the bullet + rod. I got scary and, I think, incorrect value
$$ \Delta E_\text{th} = \frac{1}{2}...
Ahh! Understand.
My confusion was that I thought that in a perfectly inelastic collision the only scalar quantity that changes is the total linear kinetic energy. After additionally consulting wikipedia, here's my mistake that I made: in the conservation of energy law it should be
$$\frac12...
My initial thought was to use the conservation of energy law since there're no external forces acting on the system bullet + rod. The rod is in rest, the bullet is moving. Then after the collision, the bullet and the rod are rotating around the pivot together, so the kinetic energy of the bullet...