A car with constant speed doing a turn Let's say we have a car with four wheels and the center of the car has a speed of 50km/h. There is no friction or air resistance. If the car is moving straight each wheel will also have a speed of 50km/h, since that's the speed of the center of the car.
If the car's front wheels would turn a little bit, then we would have uniform circular motion (since there is nothing to slow down the speed). Each wheel would have its own speed (since their radius to the center of the curve would be different for each wheel). What I wonder is if the speed of the center of the car is still 50km/h?
UPDATE
I realize that there need to be friction to turn. What I meant was that there is no friction that will slow down the speed. When the car turns there will be a centripetal force perpendicular to the car's velocity. Which should indicate that the car's speed will remain the same, but it's direction will change.
NEW UPDATE
Here's a simulation I made: https://vid.me/HYz9. The red line is the car's velocity, and the green line is the front wheel's velocity. You will notice that the red line only changes direction, whilst the green line (the front wheel's velocity) also gets a higher speed as the wheel is turned. Is this simulation accurate?
 A: You are correct that centripetal force does not affect speed.  So let us consider tangential speed, which is the speed the turning car would have if centripetal force were removed.  Linear speed = tangential speed = distance / time = (2 * pi * radius) / time. (To simplify, assume the car goes through one full circle at uniform speed.) The linear speed of the center of the car is proportional to the radius of the circle.  Likewise the linear speed of each wheel is proportional to the radius of the respective circles they traverse.
When the front wheels turn, they place not only themselves, but also the center of the car, on the circumferences of circles of differing radii.
Each wheel and the center of the car will be moving at different linear speeds, and none of them will necessarily be at the same speed they had when they were on a straight line.  Also, the rear wheels will be on different radii from the front wheels, from the center, and from each other.
If there were some way for you to measure the speed of the car's center independently of the speed of each wheel, you could intentionally keep it at 50 km/h by adjusting the rotation of the wheels.  But if the wheels connected to the power train kept turning at the original number of revolutions, the center of the car would not continue at an instantaneous speed of 50 km/h, UNLESS you carefully chose to place it on the radius of a circle with speed component of the velocity vector equal to 50 km/h.
Alternatively, you could equate linear average speed with circumferential average speed:
v = r * w, where "v" is the linear speed, "r" is the radius of a circle, and "w" is angular velocity.  
Incidentally, without friction there would be no centripetal force and neither the front wheels nor the center of the car could move in circles, as warhead pointed out.
A: I would say that indeed the center of the car still move at 50km/h. 
The angular velocity is $\omega = v/r$, with v the tangantial velocity and r the radius.
Therefore the wheels on the inside will go slower (smaller v) and the wheel on the outside will go faster (larger v) to keep the same angular velocity $\omega$.
Best, 
Samuel
