Work done by static friction during rolling while slipping? I'm a bit confused on whether, during slipping while still rotating, friction does work on the object. I know there are multiple questions on SE that address the rolling case, but this is very specific to work done by rolling while slipping.
While an object is rolling, its point of contact with the ground is still,  so there is no distance traveled, and thus no work. But what if you have a case where a circular object is pushed, like a bowling ball, and it starts rotating. You have a frictional force acting on it to create the rolling case $v = r\omega$, but does friction do work on the object? And is that frictional force constant, resulting in just $W = F_{FR} \cdot d$, where $d$ is the distance traveled from being pushed to stopping the slipping?
 A: Friction does not do the work (in a reference frame at rest with the floor), the work is done by the pushing force. The instantaneous center of rotation is the contact point on the floor. So the pushing force also provides the torque that makes the object rotate. This of course, happens in the system of reference at rest with the floor. If you look at things in an accelerated frame in which the center of the sphere is at rest, then to you is the friction that provides the work and the torque. Remember that the  work made by a force  depends on your frame of reference.
A: In case of a body slipping without rolling , this means that there is only acceleration of the center of mass (which only aids in its forward slipping motion) , for a body to roll the surface must have friction ( take the example of a car's wheel , if there were no friction the wheel would rotate in the same place and the car wouldn't move ).

Now for addressing the mathematical point of view of this question ,
Friction is a self adjusting force , it acts in the direction opposing the motion. When you accelerate an object by providing a clockwise torque (for example turning the key of a toy car) , friction acts in the direction opposite to this force providing an anticlockwise torque which helps the body to move ( Don't get confused now , friction won't completely stop the motion here unless the coefficient of friction has a value of 1)
