Why not such a car?
1. A nuclear reactor needs a certain mass of Uranium to function. No way to run a reactor with half a pound of uranium - not to create a significant amount of power.
2. There are radiations, that will later affect the metal in the car (the radiation shield and so on)
3. You need a BIG radiation shield.
4. A nuclear power plant produces nothing useful BUT HEAT. So you will have a very hot reactor core, and nothing else. To transform that heat in power, the submarines and air carriers use steam. This way, one uses a hot source (the reactor) and a cold source (the water) to create work (power multiplied by time). Now what car you could have capable to cool such a reactor? And how much steam you have to carry in your car for the transformation of nuclear heat in power? Usually the pressure in the primary (and secondary - guess what - there is a primary and secondary steam circuit) heat circuit is pretty high. And any crack in the primary steam reactor is capable of polluting the environment with radioactive waste.
5. For all the paranoids out there, one could buy 10 or 20 cars and cut open their engines. You will end with enough uranium to create a small nuke.
6. Can you imagine a car cimitery where the radiation will be equal to that in Chernobyl, by example?
7. A frontal crash between two such cars will produce radiation hazard, so everyone in a radius of 30 miles will have to be evacuated.
If you need more reasoning, send me a message.
(for the moment, I suppose the main reason against this is the sheer mass needed for a vehicle)
Calin
EDIT1:
I just RTFA and found out about the pebble reactor. So, the questions are:
How will you shut down such a reactor? If you can't, your car will just be hot all the time. Considering the current efficiency of the steam engines, you will output heat at some rapid rate - for a supposed car with 200 kW engine (271 KW) you will output three times that heat into the environment. Do you have a electric heater? It probably has a power of 2 kW. Your car will output 300 times that. Can you say red hot?
You will need a high flow of air to cool that beast. As is necessary a 50 cfm fan to cool a 100W processor, you will need a small tempest to cool your car.
Assume you could shut that reactor down when not in use (by using some kind of moderator), when running you will still have a 1 000 Celsius degree hot reactor in the car, with several pounds of 1 000 Celsius hot steam at a pressure of tens of atmospheres. In case of a small accident that will crack the heat pipes, you are toasted (or maybe boiled).
You can't use tap water. All the minerals in the water will remain inside the pipes, finally clogging them. Also reducing the power output of the engine. So, you'll most probably have to use distilled water (which is cheaper than gasoline).
EDIT2:
How much will weigh the encasing? I'll let you guess. Can you put that in a sport car? Guess again.
If the car power is 35 kW, then will you drive a car that is having only 50 HP? Guess not, considering the weight of all the systems.
If the encasing is complete, how will you have steam out of it? If only from the outsides, then you will have a huge mass of lead and titanium at 1 000 C in your car. What temperature is needed to molt lead? Yes, you're right. Molten lead.
The pebbles will maybe not contain enough uranium (not concentrate enough) to create a critical mass. However, cutting the titanium encasing is just time consuming, and not extremely difficult. However, it should be much easier to concentrate the uranium in the pebbles than to produce it from ground up (mining operations). Even so, it could be used for a radiation atack (not a nuclear one).