Why is the frictional force on a wagon's wheel in the opposite direction from the frictional force on a car's wheel?
Answer:
When you pull a wagon forward, friction from the ground starts the wheel turning and it does this by pushing backward on the bottom of the wheel. Friction is thus preventing the wheel from skidding across the pavement. When you step on a car's accelerator, the car's engine starts the wheel turning and friction from the ground pushes forward on the bottom of the wheel to prevent the wheel from skidding across the pavement. In the first case, friction is trying to help the wheel to turn while in the second case friction is trying to keep the wheel from turning. That's why the forces (and the resulting torques) on the wheel are in opposite directions for the two cases.
