Answer
Pushing the barrel with this applied force causes a frictional force to be exerted on the bottom of the barrel in the opposite direction to the motion. This frictional force creates a torque about the axis which causes the barrel to rotate.
Work Step by Step
On a frictionless surface, this force would not cause the barrel to start rotating.
However, on a surface with friction, pushing the barrel with this applied force causes a frictional force to be exerted on the bottom of the barrel in the opposite direction to the motion. This frictional force creates a torque about the axis which causes the barrel to rotate.
