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So after much pondering of the fact that the net static friction force points in the center, perpendicular the tangential motion, I thought of this explanation.

If we look at a car travelling around a circle, the wheels are always turned. There is a static friction force causing the tires to rotate, pointing in the same direction as the tires. There is also a force of static friction that causes the wheels to not slide. The wheels would like to move in the direction tangential to the circle due to inertia, and static friction also wants to stop this, so it'll oppose the inertia. This force must be acting tangential to the circle but in the opposite direction. The vector sum of these forces then must equal the centripetal force.

Is this a correct explanation? No instructor has ever explained how these two forces add together so I'm not sure if I'm correct in my thinking. Thank you!

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Remember that static friction is just one force, it has to point parallel to the surface, and it's entire reason for being is to prevent sliding. You can think of it like the force in the cogs of a gear. But you are interested in its different components, which exist for different reasons, because there are different reasons why sliding of the tire on the ground might occur. One is if the car's gas pedal is pushed, then the tire is trying to slide backward on the ground and requires a forward force on the tire to prevent that. This ultimately becomes the force that does accelerate the car. If the car is not speeding up and is suffering no air resistance or other forms of dissipation, there is not any static friction force in the direction of the car's motion.

If the car is also in a turn, then the wheels will try to slide sideways along the road, away from the center of the turn. Again the static friction force will prevent that, so this time it will supply the centripetal force on the car. So static friction is always the force that makes the car accelerate, in whatever directions it is accelerating. It is not the force that makes the wheel turn faster, however, that comes from the axle, and the frictional force opposes that.

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  • $\begingroup$ Thank you Ken! So then are the two components I stated the correct components that sum to equal the force centripetal? $\endgroup$ – rb612 Oct 9 '16 at 4:08
  • $\begingroup$ I don't quite see why there would be two components that add. The centripetal force is sideways to the road, and that is all static friction. If the car is moving at constant speed, there would need to be some kind of torque from the road to turn it, so static friction would also have to do that, but that torque would seem normal to neglect. So then there's only one centripetal force-- the inertia force doesn't count, that's just the ma term, so that is what the centripetal force equals. Centripetal force is ma, but it has to come from some real forces, here just friction. $\endgroup$ – Ken G Oct 9 '16 at 4:26
  • $\begingroup$ the issue for me in understanding is how static friction is supplying a force sideways to the road. I can see how there would be two different forces of static friction acting that would add up to be the centripetal net force, but I don't see how static friction would ever be pushing on the tire in a direction that is not at all parallel to the tire's orientation (like how with rotational motion it is parallel) $\endgroup$ – rb612 Oct 9 '16 at 5:15
  • $\begingroup$ To see that the tire's orientation is not the crucial issue, just imagine holding a tire in your hands, and trying to drag it sideways along the ground. You'll get a static friction force that will prevent the tire from moving, regardless of which direction you try to slide it, if you don't push too hard. $\endgroup$ – Ken G Oct 9 '16 at 12:27
  • $\begingroup$ Right, so we are in agreement then that there are two component forces acting on the tire that are part of the net static friction force which points centripetally: one force is allowing the tire to roll, another is preventing motion in the tangential direction. Is this the correct way of thinking about it? $\endgroup$ – rb612 Oct 13 '16 at 6:22
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No. Static friction can act to prevent tires from spinning, but at constant speed, no force is required to do this so static friction along the car's path can be zero. Static friction perpendicular to the car's path is what allows it to turn. For uniform circular motion, there only needs to be one horizontal force.

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