# Will pure rolling occur if the body encounters a frictionless surface during its motion?

i have seen that for pure rolling conditions,the point of contact has zero velocity and friction plays no roll in it, my concern is if all at a sudden the body gets a frictionless surface will it still maintain pure rolling or will start skidding, m taking rolling friction negligible and not taking into consideration.

for pure rolling conditions,the point of contact has zero velocity and friction plays no roll in it

Kinetic friction doesn't play a role, no, but static friction can certainly have a say. There can be plenty of static friction in order to hold that contact point still.

my concern is if all at a sudden the body gets a friction less surface will it still maintain pure rolling or will start skidding

It can continue the pure rolling motion, but only if the rolling very precisely follows the surface, so that the contact point still is constant. That would then be just a coincidence, since the slightest change in either rotational or linear motion would break the sync and cause the contact point to move relatively.

In the ideal case it will be the case if no other forces act horizontally on the car (no air resistance, no hills causing a tilting/non-vertical normal force etc.).

• "There can be plenty of static friction in order to hold that contact point still." Is this true for the ideal conditions in the OP post? Commented Feb 26, 2018 at 19:54
• nevermind, I guess that's what you mean in the last sentence. Commented Feb 26, 2018 at 20:02
• @TomB. No, in the case of an ideal, perfectly smooth, frictionless surface, there would be no static friction. That is the reason the wheel could free-spin and stop following the surface on the last paragrpah. Static friction is what holds the contact point still, but it can't do that without at least some friction. If you drive up a hill, then your wheels experience pure rolling but a large static friction is pulling upwards in order to hold back against gravity, so that the contact point does not slip and slide. Commented Feb 26, 2018 at 20:08
• Right, but even for an ideal, perfectly smooth, non-frictionless surface, that friction plays no role on a horizontal surface with no acceleration. I'm not sure how ideal the OP assumes the situation is. It's unusual to consider friction problems in ideal situations. Commented Feb 26, 2018 at 20:17
• @TomB. True (I'm wondering how "perfectly smooth" and "non-frictionless" can go together :) ) Commented Feb 26, 2018 at 20:33

Note that friction plays no role in pure rolling only if there is no linear or angular acceleration. I assume this is the case for your example. If so, pure rolling will continue over the ice. If there is no friction force on the rolling object, it will continue to rotate with a constant angular velocity, due to conservation of angular momentum. Therefore the contact point will remain instantaneously stationary relative to the ice. Do the following thought experiment: Gradually lift the object off the ice using a friction-less bearing at the center of the object, just a tiny bit, while it is rolling.