# Circular Motion Doubts

Hello! I have a few doubts in circular motion and I'd really appreciate your help :)

1) There is a statement in my book ( I have attached images - the first one) according to which the only horizontal force towards the center on the vehicle is friction. I know that some centripetal force is necessary for the vehicle to move in a circle..but why friction? Friction opposes motion, yes, but if there is no friction, the body will move in the direction of its velocity which is tangential. So why isn't friction opposite to the direction of the velocity? Why is the direction of friction towards the center? Also, it is mentioned that static friction acts on the vehicle. But why static friction..if the body is moving? :/

2) The second image that I have attached describes the motion of a vehicle when the road is banked at an angle θ. But it says that the frictional force keeps the value of horizontal component of Normal force zero.What do they mean by this? Does friction balance this horizontal component? IF it does, why will there be an acceleration towards the center? And they haven't even shown the force of friction in the FBD..I am really very confused :/

- I have marked the lines with an *

#### Attachments

• photo 1.jpg
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• photo 2.jpg
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## Answers and Replies

The friction force towards the centre of the circle arises because the front wheels are turned inwards. This is not obvious in the diagram. I am assuming the track is horizontal.
If the track is 'banked' it is possible for the centripetal force to come about without friction.

Doc Al
Mentor
Also, it is mentioned that static friction acts on the vehicle. But why static friction..if the body is moving?
As long as the tires aren't skidding along the pavement, the friction involved will be static friction. Realize that there is no relative motion (no slipping) between the patch of tire in contact with the road and the road. Kinetic friction requires such relative motion.

2) The second image that I have attached describes the motion of a vehicle when the road is banked at an angle θ. But it says that the frictional force keeps the value of horizontal component of Normal force zero.What do they mean by this?
I believe that it's just an awkwardly constructed sentence. They mean that the friction force is kept to zero, not the horizontal component of the normal force.

1 person
In the case of cars friction is responsible for linear motion, it is the force that pushes the car forward against air drag. In the first image we do not have a tangential force but that does not mean that there is no tangential friction force it means just that it cancels out with the air drag.In a real car things are bit more complicated because of the direction of the front wheels but in the end it is still correct to think that we have a single centripetal friction force acting on the center of mass of the car.

In the second figure they show that if the geometry is correct for some speeds and some cars there will be no tangential friction force.

you can understand the meaning correctly and app. after you study rotation torque and rolling.

Just to clarify something. Friction does NOT oppose the motion. Friction opposes the tendency of the motion of the point of contact between the object and the surface.

For example an upward rolling ball on an inclined plane is submitted to upward frictional force. In this case, the direction of friction is the same as that the whole motion of the ball, but it opposes the tendency of the motion of the point of contact.