Some questions about car radio and cellphone antennas 1-Why the antenna of the radio of cars is located outside the car and not inside?
2-If the answer to 1 is because that cars are like Faraday cages then how come my cell phone can receive signal inside the car?
3-To receive a strong tv/radio signal the antenna must be oriented in a specific way. Why the strength of the cellphone signal seems independent of the orientation of the cellphone?
4-It seems to me that the length of the antennas of cell phones or that of a tv or radio is of the same order as the corresponding wavelength used, why is that?   
 A: (I'm not exactly sure of this, comments greatly appreciated)
Radio waves have a longer wavelength (3-4 m) than cell phone waves(fractions of a meter). Thus these are easy to block. They can travel around  buildings &c, but can't enter cars because the windows are tiny. Cell phone waves are small enough to enter the windows of a car.
Radio waves have large antennae due to their wavelength. So reorienting them makes a difference as the effective size of the antenna facing the wave changes drastically. A cellphone jas a tiny antenna. Reorienting it makes little difference. Imagine making the antenna shorter and shorter till it becomes a ball. Reorienting that makes no difference at all.  And a cellphone does change quality on rotation, but its less evident. There may be some smoothing circuitry involved.
Edit: Antennae need to be with the same order of magnitude as the radiation as they need to resonate. See http://enwp.org/Antenna_(radio)#Resonant_antennas . A short antenna cannot effectively acheive resonant frequency of a long wave.
A: 1- FM radio waves are several meters long and so your car 'looks' like a solid metal box to them. 
2-  Cell phone radio waves are a few 10cm long and so the car looks like a box with large holes. In addition cell phones have a lot of clever circuitry and digital coding to ensure that they can receive a very weak signal and so can cope with any signal loss a lot better than a simple  FM radio
3- Modern cell phone antennae are designed on the assumption that you will hold the cell phone at any angle and so have complex antennae designs that work in all directions.  Car radio antennae are mostly simple rod antennae .
4- Car radio antennae are dipoles they are simply metal rods designed with a length to match a fraction of the radio wavelength. In simple terms when the radio wave is a peak at one end it is a trough at the other and so there is an electric field and so a current 
flows
A: 1 - The main reason is that your car RESEMBLES (not IS) a Faraday cage (even though, hey, we are talking about 10 meters - the smallest - wavelength here! The wave doesn't exactly "see" the car - it sees a material that is a mix of air, metal and silica). In the car, there are also electronics that COULD also produce noise... But it wouldn't be the main issue.
2 - Your car is NOT a Faraday cage. Even if shorter waves (GSM, UMTS, LTE, Wi-Fi, Bluetooth) DO "see" your car as a "shield", it is not a Perfect Electrical Plane. Of course, the radio waves get attenuated, but yet you have a signal. On top of that, silica (windows) is not metallic at all, so the waves "see" giant "holes".
3 - This is not quite true: you normally need to orient a DIRECTIVE antenna. The OMNIDIRECTIONAL ones radiate almost in the same way in every direction. Provided that the antennas in your cell phone are not ARRAY ANTENNAS, their radiation is quite similar to an omnidirectional one... Except that for obvious reasons, they won't radiate to the front of the phone (or your head). Please notice also that the current generation of mobile phones have a chipset that allows them to adjust power in order to maintain a stable connection... The meaning is: your phone always has a signal - but you can't see the power output that grants that (trust me, it changes).
4 - This is absolutely wrong. There are millions of kinds of antennas and the specs depend always on their purpose. Car antennas (smallest wavelength = 10m) are not 5m length. That is because nowadays we attach active elements to them as well as implement different shapes in comparison to a normal dipole (car antennas are in fact an excellent example). Finally, there is a wide range of PATCH-ANTENNAS whose radiation frequencies are mostly proportional to the length of their sides (but don't take this strictly as a law).
Source: Trust me, I am an engineer... And I work with antennas
A: *

*You guessed right. Faraday.

*Then how come you can see anything outside when you're in the car? Light is also electromagnetic radiation, no? The answer is - the car as a "Faraday cage" works different at different frequencies. It damps the FM signal quite a bit (not completely, my portable FM radio still works in the car, just not as good), it damps the higher frequency cell phone signal a little bit less, it doesn't do much against visible light (except by direct obstruction).

*It's not independent. Move the phone around and the signal strength will change. Complete extinction of the signal is darn near impossible to achieve in real life, even when both source and receiver are near-linear polarized. The field usually has too many kinks for that to happen.

