Suppose a cylinder is launched on a horizontal frictional surface such that it has initial translational velocity $v$ and zero angular velocity. the kinetic friction would be applied between the contact points of the cylinder and the surface, opposite to the direction of the translational motion. This kinetic frictional force will simultaneously apply torque on the cylinder (which will increase its angular velocity) and decrease the translational velocity till the cylinder satisfy the condition for pure rolling($V=RW$). when the condition for pure rolling is satisfied, the relative velocity between the contact points and surface would be zero and this there would be static friction between the contact points and the surface.
My confusion is that why is static friction necessary for pure rolling instead of kinetic friction. Static friction is applied when the object satisfies the condition for pure rolling ($V=RW$). The static friction does not increase or decrease, both translational and angular velocity. Kinetic friction on the other hand ensures that the object follows the condition for pure rolling on a horizontal frictional surface.
According to my understanding, if an object is launched on a frictionless surface such that it initially satisfies the condition for pure rolling, then the object would continue to be in pure rolling motion even in the absence of static friction(static friction=0 because µ=0), thus the static friction is not necessary for pure rolling. But if an object is launched on a frictionless surface such that it initially does not satisfy the condition for pure rolling, then the motion of the object would not be transformed into pure rolling due to absence of kinetic friction. Can you explain that why is the static friction is called to be necessary for pure rolling of an object instead of kinetic friction?
Best Answer
The short answer has already been given to you in some of other answers. Pure rolling involves no slipping and kinetic friction only exists where there is slipping.
That said, kinetic friction can play a role in establishing the conditions to initiate pure rolling and does play a role when there is "impure" rolling, i.e., a combination of rolling and slipping. I will attempt to explain by individually addressing a number of statements in your post.
Static friction may or may not be needed for the condition of pure rolling, depending on the circumstances, as discussed below.
For the example you provided, static friction would not be needed for continued pure rolling once the condition $v=R\omega$ for pure rolling is satisfied. Exactly what happens will depend on whether or not the horizontal launching force continues to be applied or is removed after motion is initiated, as discussed below:
Once the launching force is removed, in the absence of other external forces (e.g., air drag, rolling resistance), the only horizontal force acting on the cylinder is kinetic friction which reduces $v$ and increases $\omega$ until the condition $v=R\omega$ for pure rolling occurs. At that point there is no kinetic friction (since there is no slipping during pure rolling). There is also no static friction since static friction only exists in opposition to an applied external force, of which there is none. The cylinder will continue to roll without slipping at constant $v$ and $\omega$ due to its inertia.
Since the horizontal launching force caused slipping, that means the launching force exceeded the maximum possible static friction force of $\mu_{s}mg$ so that friction transitions to kinetic friction only. That leaves only the kinetic friction force and the horizontal launching force $F$ applied to the cylinder. You will now have a condition under which both slipping and rolling occurs, or "impure" rolling if you will, with the angular acceleration determined by the net torque about the COM.
As already pointed out static friction is not involved in the example you gave because the initial launching force exceeded the maximum possible static friction force. Only kinetic friction is involved during and following launching as long as there are no other external horizontal forces acting on the cylinder.
Now if, instead, the launching force did not exceed the maximum possible static friction force of $\mu_{s}mg$, then no slipping would occur and static friction would apply a torque about the COM. Once again, the angular acceleration would depend on the net torque about the COM. That, in turn, would depend on the location of the applied horizontal force relative to the COM.
Again, kinetic friction never insures pure rolling because kinetic friction only exists when there is slipping. Kinetic friction may insure a combination of rolling and slipping.
In order to initiate pure rolling of the cylinder on a frictionless surface, the applied horizontal force would need to generate a torque about the COM since there would be no friction force to generate a torque. That is, the applied horizontal force needs to be applied either above the COM to generate pure clockwise rolling, or below the COM to generate pure counter clockwise rolling. If it is applied to the COM the cylinder will simply slide without rolling.
The launch on a frictionless surface will not satisfy the condition for pure rolling only if the applied horizontal force is applied to the COM, since there would be no torque about the COM.
But kinetic friction can only initiate pure rolling by satisfying the condition $v=R\omega$. It cannot maintain pure rolling where friction is needed to maintain pure rolling. That's because kinetic friction only continues to exist if slipping is occurring. Only static friction maintains pure rolling where friction is needed to maintain pure rolling.
Hopefully my comments above taken together have answered your question.