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I encountered this diagram when reading an explanation about why the front wheels of cars lift up when they accelerate. The diagram is in the reference frame of the car, so that there is a fictitious force $MA$ on the center of mass. $f_1$ and $f_2$ are the frictional forces on the wheels. Now the car is not moving backwards and accelerating forwards. It is moving forwards and accelerating forwards. So when viewed from an inertial frame, $f_1$ and $f_2$ should point opposite to $A$, right? Yet why does it point in the same direction as $A$ in the reference frame of the car?

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  • $\begingroup$ This is a pic that i use: i.stack.imgur.com/WxubU.jpg it may help. $\endgroup$ – Bhavay Jun 30 at 7:49
  • $\begingroup$ That still doesn't explain the direction of $f_1$ and $f_2$ in your diagram $\endgroup$ – Brain Stroke Patient Jun 30 at 8:19
  • $\begingroup$ Imagine the bike to be at rest. U push the pedal , the back wheel moves to rotate (clockwise) to stop that $f_1$ acts forward , now the whole back will accelerate forward due to $f_1$. Now come to $f_2$ . Since the whole bike along with rear wheel moves forward friction at rear wheel acts backwards . $\endgroup$ – Bhavay Jun 30 at 8:51
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We aren't interested in the bulk motion of the vehicle, only the relative motion of the part of the car touching the road (the bottom of the wheel).

It's often useful to imagine what would happen if we turned friction to zero. We'll let the car move forward a bit and then turn it off.

As the accelerator pedal is pressed, the wheel will slip and spin forward. Looking at the ground, the bottom of the wheel moves backward relative to the ground. So when friction returns, the force appears opposite to the relative motion of the tire, and it points forward.

Another way to see this is that a car rolling forward may be coasting (no frictional force), accelerating (friction accelerates the car forward), or braking (friction accelerates the car backward). You can't tell the direction of friction by looking at the speed of the car.

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  • $\begingroup$ Why doesn't friction work like that when a wheel is rolling without slipping while descending an inclined plane though? In those cases even though the wheel rotates backward relative to the ground, the friction is still backwards. $\endgroup$ – Brain Stroke Patient Jun 30 at 9:08
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    $\begingroup$ The difference is what is driving the wheel. If the wheel is pushed forward (gravity, big hand, etc), then friction is causing the rotation and pointing backward. If instead the wheel is turned (by an engine), then friction is slowing the rotation and pointing forward. In both cases imagining what would happen in the zero-friction case gives insight. A wheel sliding down a hill has the contact patch moving forward on the ground. An engine spinout moves the contact patch backward against the ground. Friction will oppose both motions. $\endgroup$ – BowlOfRed Jun 30 at 15:30
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Frictional force, and any other force for that matter, is the same in an inertial and a non-inertial frame of reference. In the non-inertial frame, only an extra force $-MA$, called the pseudoforce or fictitious force is necessary to get the correct equations of motion.

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  • $\begingroup$ So even in an inertial frame, the frictional force would seem to point to the right? But why? If the car is moving to the right, then friction should act in the left direction in my diagram. $\endgroup$ – Brain Stroke Patient Jun 30 at 8:39
  • $\begingroup$ Frictional force always tries to stop the relative motion between two surfaces - in this case the wheels of the car and the road. As the car is moving towards the right, the wheel is moving clockwise. Therefore, the lowest parts of the wheel is moving towards the left with respect to the road. Therefore, the frictional force acts towards the right. $\endgroup$ – abir Jun 30 at 8:44
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For the vehicle to move in the direction pointed to by A, the wheels have to rotate clockwise in the reference image. Thus the direction in which the wheels push the ground is opposite to A and consequently the ground pushes the wheels or you could say the entire car frame in the direction of A (3rd Law). These are the forces f1 and f2 depicted in the image. Note that we always show those forces which are acting ON our frame of reference by elements outside the frame, which is the road in this case providing friction.

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  • $\begingroup$ I'm not so sure about that. If that were the case, then why doesn't friction work the same way for a wheel rolling without slipping? This answer has a diagram of direction of friction and rotation which doesn't follow your reasoning. $\endgroup$ – Brain Stroke Patient Jun 30 at 6:58
  • $\begingroup$ @BrainStrokePatient, that diagram doesn't have any torque from the engine applied. If you push the car forward (say with a tow truck), the direction of friction is opposite than if the engine were driving the car forward. $\endgroup$ – BowlOfRed Jun 30 at 8:46

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