I came across a question which says:
"A force $F$ acts tangentially at the highest point of a sphere of mass m kept on a rough horizontal plane. If the rolls without slipping , find the acceleration of the centre of mass of the sphere."
The equations in the solution are:
For translational motion,
$F+f=ma$
For rotational motion about centre,
$Fr-fr=I{\alpha}$
where $f$ represents frictional force, $a$ is linear acceleration of the sphere and $\alpha$ is angular acceleration of the sphere, $r$ is the radius of the sphere.
At first I thought that the surface would provide friction to the left side for bothe translation and rotation of the sphere, but was only amazed to look at the reason given in the solution.
The reason is given as -
"As the force $F$ rotates the sphere, the point of contact has a tendency to slip towards left so that the static friction on the sphere will act towards right"
Is it the correct explanation?
Also I wanted to make sure whether tangential force always tends to slip a sphere in opposite direction and static friction acts towards direction of that tangential force.