Can an object roll without slipping if friction is the only horizontal force applied In my physics class, we only considered rolling without slipping in examples when friction wasn't the only external force on an object, and I was wondering if it was at all possible for static friction to be the only force acting on an object that's rolling without slipping (and the rotational kinetic energy changing to compensate for this would violate the no-slip condition).
I believe the answer is no, because the translational speed would have to change because of Newton's second law, but the kinetic energy has to remain the same because friction does no work on a non-slipping object.
Setting up the equations gives
$$F_fR=I\frac{a}{R}$$
$$F_f=ma$$
Which then implies that $$m=\frac{I}{R^2}$$ Which doesn't hold for all objects.
Any insight on this?
 A: I assume you mean something like the only horizontal force.  We can't get static friction in the first place without some normal forces being present as well.
But static friction never arises on its own.  It's always alongside other forces.  This doesn't matter if it's rolling without slipping or just a box sitting on a table.
Given an object on a table with no non-frictional horizontal forces, you will either have kinetic friction to slow the object or the object will be sitting still with no frictional forces at all.
The same is true for a rolling object that is not slipping.  Static friction disappears with no forces for it to oppose.  It will continue to roll without slipping as well.
A: Generally static friction has a maximum possible magnitude that is proportional to the normal force.  If the normal force is zero, the static friction cannot be anything other than zero, so strictly speaking, it is not possible for static friction to be the only nonzero force—there must at least also be a normal force.
Perhaps your intent is to ascertain whether it is possible to have rolling without slipping when the contact force is the only force.  The contact force is usually decomposed into normal and frictional components, but really it is just one force, and it is certainly possible to roll without slipping with no forces acting on the rolling object aside from this one.
As an example of this, take a small ball rolling around the inside of a cylindrical shell, with no gravity. The only force on the ball is the contact force. By applying appropriate accelerations to the shell, the ball can be made to speed up or slow down, all while rolling without slipping, and with no force but the contact force (including a frictional component) acting on the ball.
