when an object is rotating in a circle and the only force is acting on it is friction how is force of friction vector pointing towards the circle because an object in circular motion is traveling in that direction, it's accelerating towards the center of the circle, but friction is suppose to appose motion... and if motion is towards the center of the circle how could friction alos be if it's suppose to oppose motion

Friction is not towards the center, it is directed against the motion, tangentially.

Now for motion in a circle. Motion in a circle is NOT directed towards the center, or it would spiral inward. In a constant radius circle, ACCELERATION is directed inward, and that is why the object does not travel in a straight line.

When an object is rotating in a circle and the only force acting on it is friction, the force of friction is directed towards the center of the circle. This may seem counterintuitive, as friction is usually thought to oppose motion. However, in this scenario, friction serves a different purpose.

To understand why friction acts towards the center of the circle, let's consider the forces involved in circular motion. Circular motion occurs when an object moves along a circular path at a constant speed, which means there must be a force acting towards the center of the circle. This force is called the centripetal force and is required to change the direction of the object's velocity, keeping it on its curved path.

Friction between the object and the surface it is moving on provides the necessary centripetal force. In this case, the frictional force points towards the center of the circle to provide the inward force required to keep the object in its circular path. This inward force acts as the centripetal force, ensuring that the object continues to move in a circle rather than moving in a straight line.

It's important to note that friction opposes relative motion between two surfaces in contact. In the case of circular motion, there is no relative motion between the object and the surface it's moving on in the direction perpendicular to the surface. Therefore, friction can act in the inward direction towards the center of the circle without violating its nature to oppose motion.

In summary, when an object is rotating in a circle and the only force acting on it is friction, the force of friction is directed towards the center of the circle to provide the inward centripetal force required for the object to maintain its circular path.