Q.29. A force F is applied at the top of a ring of mass M and radius R placed on a rough horizontal surface as shown in figure. Friction is sufficient to prevent slipping. The friction force acting on the ring is -

(1) $\frac{F}{2}$ towards right
(2) $\frac{F}{3}$ towards left
(3) $\frac{2F}{3}$ towards right
(4) Zero

Option d

Option d Can pure rolling (without slipping) happen without friction? Is friction in pure rolling always static? Pure rolling is a situation when there is no slipping while rolling. This can only occur when the contact point of rolling object with the surface is having zero velocity. It occurs when velocity due to translation motion exactly cancel out the velocity due to rotation motion. This will happen when (V = w x r) where w is angular velocity and v is translation velocity ( velocity of center of mass). so at the contact point v will exactly cancel out the wxr. Now if rolling motion is started with the above condition satisfied then no relative motion with respect to surface. So friction will not appeare, even if it is not a smooth surface. So in this case you can have pure rolling without any friction. But if you start the rolling without above condition satisfied then the contact point will not have the net velocity zero so there will be slipping either backward or forward. Now in this case if surface is frictionless, there would not be any torque/ force which can bring the velocity (v) equal to w x r and pure rolling will not occur. We can say pure rolling can occur without friction depending upon how you have started. Now whether friction will be static or kinetic will depend upon what is the condition. If your contact point is not have net velocity zero the friction would be kinetic. And if your contact point is having zero velocity than there would not be any friction at all. But if there is any external force which wants to alter the velocity then first the static friction will come into picture as the contact point is at zero velocity. 1.6k Views · Once an object starts rolling on a horizontal surface, there is anyway no need of friction unless it needs to accelerate (this is all theoretical, in reality, rolling friction is involved on account of deformation). So, you don't need friction for pure rolling without slipping to occur. -- Hope this answers your query and puts some more questions in your mind. 4.1k Views · · Answer requested by Your feedback is private. Is this answer still relevant and up to date? Theorotically yes! When you put a rolling wheel( with velocity of center of mass exactly equal to radius X velocity ) on a perfectly frictionless surface, then the only forces acting on the wheel are : 1) the normal reaction. Since the normal reaction is perpendicular to the contact surfaces, it will be radial to the wheel. Since the force vector is parallel to the vector from its center to the point of contact, the torque of the normal reaction will not affect the angular velocity of the body. 2) gravitational force. The gravitational force can be assumed to be acting on the center of gravity( why? ) and acting perpendicular to the ground. Since this vector is also parallel with the radius vector, its torque will also be 0. In absence of torque, the angular velocity will never decrease. Now we do realize that such surfaces are very hard to create as there will always be roughness at the molecular level( or at least till now! ) ( Thanks to for pointing out that any other velocity will cause rolling with sliding ) To your second part of the question : No. A kinetic friction will also cause rolling. The kinetic friction when applied to a wheel will decrease its linear velocity but increase its angular velocity( friction is parallel to surface and hence provides a non-zero torque ). Try kicking a football( so that you don't impart angular motion ) and see if it rolls on the ground before stopping :) 8.2k Views · · Answer requested by Your feedback is private. Is this answer still relevant and up to date?