Problem statment: A rod hinged at one end is released from the horizontal position. When it becomes vertical its lower half separates without exerting any reaction at the breaking point. Then find the maximum angle $θ$ in degrees made by the hinged upper half with the vertical.
Approach:
Let $w$ be angular velocity
Use energy conservation to get $w_1=(3g/l)^{1/2}$
Now, as there is no external torque acting when the rod is vertical, angular momentum must be conserved (according to me).
So $w_2 = 8*w_1$ ($Iw=const$)
Use energy conservation again.
We get $cos(\theta) = -3$ which is definitely not right
However, if we assume angular velocity to not change will land to the answer which is $60°$
I just need a reason for the angular velocity to not change, I know how to proceed.
PS: Sorry for bad formatting, I am new here.