I know that static friction isn't the cause of deceleration of a rolling body. But if static friction is the only force in the horizontal direction, then shouldn't there be some acceleration produced in this direction? The body should decelerate or accelerate. So how come in this case, a force does not produce acceleration?
Please help! I have been pondering on this question for a long time.
When a disk or other object is rotating on a horizontal surface with constant velocity, there is no static frictional force. Your logic is correct: if there were a horizontal force, the center of mass would be accelerating.
If the rolling object suddenly encounters a frictionless surface, it would continue to satisfy the rotating without slipping condition. Friction is not required to keep the object rotating. Once it gets rotating (which might indeed require friction), it'll continue to rotate unless a net external torque acts on the object.
Here's my explanation (hopefully it's right but I'm no expert):
Consider the simpler example of pushing a really heavy box; if we push on it there's a static friction force, but if we don't push on it there's no force. Similarly for a cylinder on a horizontal plane, if we push on it the static friction force causes it to rotate, but when we stop pushing there's no static friction force but it keeps moving because no other force is there to slow it down. The static friction only arises in response to our push.
Let's say you roll a ball (of mass $m$) down an inclined plane of angle of inclination $\theta$ and coefficient of static friction $\mu_{static}$. Then you know a force parallel to the inclined plane acts on the ball through its center of mass. Another force parallel to the surface acts in the opposite direction of motion as follows,
The force $\vec F = mg\sin\theta$ , $\vec N$ is the nomal reaction and $\vec f$ is the frictional force.
$\vec F$ and $\vec f$ act in opposite directions as shown in the figure. These two forces produce a couple (or torque) which makes the ball rotate. However, irrespective of their point of application, they act in opposite directions on the center of mass and so may or may not produce an acceleration.
If $\vec f \ge\vec F$, then there will be no acceleration, otherwise there would be.
However as you are asking of the case when the only horizontal force is the frictional force, you should know that there won't be any friction at all if you are talking about pure rolling. This is because, the velocity of the lowermost point (or the point of contact) in case of pure rolling is $0$ and so there is no impending motion of the lowermost point.
The velocity $\vec v$ and $\vec\omega R$ are equal and acting in opposite directions on the lowermost point. As a result, its velocity is zero resulting in zero friction. So in an ideal situation such as this, there will be no static friction, so clearly there will be no deceleration or acceleration.
You might ask what do I mean by an ideal situation. Well, in this case, we are considering pure rolling which happens only if there are no momentary deformations of the surface of contact. Now, this does happen in real life, so, there is a friction acting in real life and that is why the ball slows down.
In general static friction changes the velocity of a rolling body in order to maintain the condition that the contact point is istantaneously at rest. For a homogeneous rigid body with cylindrical symmetry around the rotation axis this condition is $$v_{cm}+\omega R=0,$$ $v_{cm}$ is the velocity of the rotation axis, $\omega>0$ counterclockwise, $v_0>0$ towards right.
Due to static friction a body rolling down an inclined plane has a linear acceleration smaller than the same body frictionless slipping. For an horizontal plane this condition is maintained without the need of static friction, as the sum of external forces and torques is zero.
A real rolling body undergoes deformations due to the reaction from the ground at the contact point. It dissipates rotational kinetic energy, reducing the "average" $\omega^2$ but not $v_{cm}$. To maintain a slipless contact a static friction is needed, that slows down the center of mass of the body.
Deformations of the ground and the body lead to a reaction force from ground with an horizontal component. This is present also for non rolling bodies. Based on energy considerations this component is going to be opposite to the center of mass velocity.
Static friction arises only when there is a mutual force between the two objects. For example, a book lying on a horizontal table experiences no horizontal force and no static friction. The same is true for a object that is rolling under ideal conditions. There is no horizontal force between the object and the surface.
