Why Does Friction Provide Centripetal Acceleration in Circular Motion?

[Lnewqban]

When I turn the wheels, ...

How the particle moving around a circular track described in post #1 ended up having wheels and a steering mechanism?

Please, see:
https://en.m.wikipedia.org/wiki/Camber_thrust

 

[A.T.]

I can't grasp how from this friction will act radially inwards?

What static friction opposes is the relative motion at contact that would occur if there was no friction (marked red in the diagram).

 

[A.T.]

How the particle moving around a circular track described in post #1 ended up having wheels and a steering mechanism?

See post #3:

but why and how does friction cause a car to turn?

 

[Physics guy]

Picture a runner in the right direction, let the runner plant his left foot on the floor, he is exerting a force down and backward on the floor, the left leg stays in contact with the floor for a few milliseconds, and the right leg is in mid air, after those milliseconds, the force exerted exceeds the maximum limit of static friction and slippage occurs. By Newtons third law, the ground exerts an equal and opposite force on the runner but do we identify this force as static or kinetic friction

You seem to be confused that friction is a reaction force to the force you apply to move any object. In fact it is not. It is a force that occurs due to electromagnetic interaction between the 2 surfaces in relative motion. In fact if you were to take an object to outer space and push it, it is not friction that is reacting to your push (because action reaction pair always act on different bodies) it the push of the object on you. You can see that you will be pushed backwards when you try to push the object forward in space. This can be recreated by standing on a roller skate and trying to push the wall, you seem to go backward even though you push the wall forward, this is the reaction force that the wall exerts on you when you exert a force on the wall.

 

[Vigorous]

As I turn the wheels to the left the wheels are pushing to the right against the floor. Friction allows the floor to push back against the wheels allowing them to turn left. If there was no friction then the object would fly off the circular trajectory and continue in the direction of the tangential velocity.

 

[A.T.]

If there was no friction then the object would fly off the circular trajectory and continue in the direction of the tangential velocity.

Yes. the car would move tangentially. But the relative motion between road and the bottom of the rotating wheel would radial (red arrow below). If present, static friction opposes that motion, and acts radially, thus providing a centripetal force to the car.

 

[Physics guy]

As I turn the wheels to the left the wheels are pushing to the right against the floor. Friction allows the floor to push back against the wheels allowing them to turn left. If there was no friction then the object would fly off the circular trajectory and continue in the direction of the tangential velocity.

Yes you got it right

 

[Lnewqban]

... If there was no friction then the object center of mass of the object would fly off the circular trajectory and continue in the direction of the tangential velocity.

... the center of mass of the object.