Perhaps a dumb question to ask, but I was given the following problem to solve:
A 10 g bullet traveling at 400 m/s strikes a 10 kg, 1.0-m-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open. What is the angular velocity of the door just after impact?
When I saw this problem my first attempt to solve this was to use conservation of energy: $m_b$=mass of bullet
$m_d$=mass of door
$L$=length of the door
$I=I_{bullet}+I_{door}= \frac 13m_dL^2+ m_bL^2$
$\frac 12m_bv^2=\frac 12Iw^2$
$w=\sqrt{\frac {m_bv^2}I}$
which is far off from the actual answer. Now, I know that the correct method of solving this type of problem is to use conservation of angular momentum, which will give:
$m_bvL=Iw$
$w=\frac {m_bvL}{I}$
Why is the first method wrong? Thanks in advance.