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The body moves on a circular path and has both tangential as well as centripetal acceleration. Friction acts outward as shown in figure. If this friction exceeds mv²/r, then shouldn't the body just move outwards instead of moving tangentially. What causes it to move tangentially. (Shouldn't it move along AB instead of AC)enter image description here

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  • $\begingroup$ ”Friction acts outward” No. consider what happens if the vehicle hits a slippery patch: it’s motion changes because friction is no longer acting, and that change take it outward which means that friction was acting inward. $\endgroup$ – dmckee --- ex-moderator kitten Aug 26 '19 at 15:22
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You have a few misconceptions. The friction which you draw in the AB direction actually acts in the opposite direction, toward the center of the curve. This friction component is the force component which has magnitude of precisely $mv^2/r$. That $mv^2/r$ value simply tells the magnitude of force necessary radially in order to travel a certain curved path at a certain speed. It is not a separate force (in the inertial reference frame of the road surface. Let's not get inside the car!).

If the car is accelerating tangentially, then the friction component between the tires and the road, parallel to the velocity of the car, is causing the car (the precise set of interactions is beyond the scope of this question) to go faster or slower.

If the maximum static friction available ($\mu_s \times $ normal force between car and road) is less than $mv^2/r$, the car will slide outward. Remember that static friction is always exactly what is needed to prevent sliding as long as the need is less than the maximum available.

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  • $\begingroup$ If the car is accelerating tangentially, then the friction component between the tires and the road, parallel to the velocity of the car, is causing the car (the precise set of interactions is beyond the scope of this question) to go faster or slower. Isn't this the same friction which causes the centripetal acceleration. How does it cause both centripetal and tangential acceleration? $\endgroup$ – McFluff Aug 26 '19 at 16:47
  • $\begingroup$ @McFluff Notice in the first 2 paragraphs I talked about the components of the total friction vector. The total friction vector actually would point at some non-perpendicular direction compared to the velocity. We don't know this direction until we calculate the individual components. Also, keep in mind that the $\mu F_N$ calculation is a simple model for friction magnitude. $\endgroup$ – Bill N Aug 26 '19 at 19:26

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