How do rudders work? It is possible for a boat to use rudder to make a U-turn while coasting (moving by inertia), although it would lose some speed. 
How exactly do boats trade a portion of magnitude of the initial linear momentum into a direction change? I would expect that the only force there is friction which would only reduce magnitude of the momentum, but it is actually changes its direction.
It must have to do with rudders, but I must admit I don't understand how they work.
 A: If you consider a boat moving through water, or alternatively a stationary boat, with water flowing past it, then the water has a momentum relative to the boat.

The blue circle is supposed to show some small volume of the water of mass $m$. If the velocity of the water relative to the boat is $v$ then the momentum of this bit of water is $p = mv$.
Now look closely at the rear of the boat where the rudder is:

The water that hits the rudder is deflected so it moves in a different direction. Now momentum is a vector, so if the direction of flow changes the momentum of the water must change. The lower diagram shows this calculation. If we once again consider our small volume of water of mass $m$ it's original momentum is $mv$ and the new momentum is $p' = mv'$. The change in momentum is the vector $\Delta p$.
But Newton's laws tell us the the rate of change of momentum is just force:
$$ F= \frac{dp}{dt} $$
This means that changing the direction of the water produces a force in the direction of the vector $\Delta \vec{p}$, and this force is what pushes the rudder, and the rear of the boat, sideways and turns it.
If the rudder was perfect it would just change the direction of flow without changing the velocity of the water. In real life there is always turbulence in the lee of the rudder and this turbulence dissipates energy and creates a drag that slows the boat down.
A: There are two separate things at work here, the first is the rudder itself which changes the boat's facing. The second is actually the keel of the boat. This is what keeps boats moving in a straight line and is why a boat can do a "u-turn". The rudder turns the facing of the boat, because the keel makes it much easier for the boat to move forwards through the water rather than sideways this also causes the direction of movement to change as the boat rotates.
