Question about circular motion of car turning When we move round a roundabout there is a frictional force between the tires and the road that acts towards the centre of the roundabout in order to produce the circular motion. Why then do we experience and outward force as a passenger inside the car?
Also how do we know exactly that the force acts towards the centre and velocity is at right angles in circular motion?
 A: During uniform circular motion, at every instant you have a velocity perpendicular to the radius (think about this like you just want to go in a straight line and some force makes you do this circular motion), meaning that the direction of your velocity changes. So there must be some acceleration that gives you that velocity component towards the centre: 
From this acceleration towards the centre, we conclude that there must be a force that causes this acceleration.
For an observer just standing on the road looking at you, you do not experience any kind of outward force. From their point of view what happens is similar to this: 
Just like the ball you want to go in a straight line but when you reach the bottom of the tube the wall of the tube pushes you back, in your case its the car, so you experience the reaction force of the car. 
A: A Force is required for any body to accelerate. As you said, the friction between the road and the tires of car cause it to move it in a circular path. But a force is also required to be acting on our body to make it move in that circle. And this force is provided by the friction between our body the seats. If this friction force is not enough to make our body move in circle with the car we would tend to fall outward, because we do not have enough force on our body to accelerate with the car. This is why we fall outwards in a turning car.

Also how do we know exactly that the force acts towards the centre and velocity is at right angles in circular motion?

This is true only if the body is moving in a uniform circular motion. The force could have components that are along and perpendicular to the direction of velocity of the body. The former, which is the tangential force would increase/decrease the speed of the body and the latter, which is called the centripetal force would cause it to move in a circle.
In case of uniform circular motion, the speed remains the same and so the force could not have any component in the direction of velocity because if it did speed would change. That's why it is perpendicular to velocity.
