Why isn't momentum conserved from my reference frame? Two cars of mass $m_{1}$ and $m_{2}$  collide with each other in a completely inelastic collision. So after the collision they continue to go in same velocity. Now suppose I am in one car. So I will consider myself stationary, so my velocity will be $0$. And the other car's velocity relative to me will be $v$. 
Now after the collision, I will still consider myself stationary and so my velocity will still be $0$ and the other car's velocity relative to me also will be $0$. 
So the total initial momentum $p_{i}$ will be:
$m_{2}v$
And the final total momentum $p_{f}$ will be $0$ 
So clearly momentum isn't conserved. Clearly I am wrong. Why isn't momentum conserved from my reference frame?
 A: You accelerated during the collision, so your reference frame is not inertial. The usual conservation laws only apply in inertial frames, unless you account for the fictitious forces and fictitious work created by the acceleration of the reference frame. Fictitious forces, if not accounted for, can make it look like energy comes from nowhere or disappears, when in reality the energy is being used to accelerate the reference frame.
A: But you will feel an impulse,
dp = Fdt
A force is being applied, which results in acceleration, as a result your reference frame will not be an inertial frame of reference (if you somehow manage to stay in a fixed position relative to the car), so momentum will not be conserved in your frame of reference
A: Your rest reference frame has changed by the collision. This is what makes collisions so dangerous. Momentum is different as determined from different reference frames, as it transforms as a vector. In each reference frame, before and after the collision, momentum is conserved. 
