A constant horizontal force Fapp of magnitude 10N is applied to a wheel of mass 10 kg and radius 0.30m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its centre of mass has magnitude 0.60m/s2. In unit vector notation, what is the frictional force on the wheel?
The figure in the book shows a wheel on a horizontal surface with the arrow representing the applied force pointing horizontally to the right from the centre of the wheel.
The Attempt at a Solution
I arrived at an answer of F = (4.0N)i. The correct answer is negative. Having given the matter some thought, this is my reasoning. In order for the wheel to rotate when the force is applied, the point on the wheel in contact with the surface must be pushed to the left by the force of friction. That explains the negative sign.
However, let's assume instead that the wheel is moving under the influence of a torque applied to centre, not a horizontal force. Now I'm visualizing the bottom of the wheel pushing against the surface to the left. If the wheel does not slip, the frictional must be countering slipping by pushing to the right.
Is my thinking correct or do I have it back to front?