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Can someone help me in understanding why there is no centripetal force acting on a vehicle while taking a turn?

Basically, my physics teacher used a non-inertial frame where the frame was at the centre of the turn but if the observer was from ground frame, then he would have seen that the car is rotating and would have a centripetal force.

To be more specific, if these type of questions are solved in accordance to ground frame, then will there be centripetal force and no centrifugal force?

ACB
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UNDEFINED
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    There is a centripetal force, it is the friction or if the road is banked, friction+normal force. – ACB Sep 01 '21 at 14:17

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The centripetal force from the road doesn't vanish in either frame. The difference is that there's another force in the rotating frame that cancels it out.

Suppose we have a car driving in a circle on a flat track at a uniform speed. In the ground frame, there is a force of friction pushing the car towards the center of the circle, with a magnitude of $m v^2/r = m r \omega^2$. Thus, the car executes circular motion in the ground frame. Note that when any object executes circular motion, the object is accelerating (its velocity is changing in direction, if not in magnitude), and so there must be an "unbalanced" force acting towards the center; this is what we call a centripetal force.

In a frame rotating with the car, there is still a frictional force pushing the car inwards, with the same magnitude as in the ground frame. However, in this frame there is also a centrifugal force with magnitude $m r \omega^2$ pointing outwards. These two forces cancel out exactly, and so the car remains at rest in the rotating frame.

Michael Seifert
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  • i got your point but can you explain me with the help of ground frame that which force is balancing the frictional force{centrifugal},so tis not falling inwards and if the vehicle skids, then which forceis responsible for it if we are talking about ground frame since no force is acting radially outwards in ground frame – UNDEFINED Sep 01 '21 at 14:37
  • @UNDEFINED not sure about your terminology but if by "falling inwards" you mean "accelerating in the direction towards the centre of the curve" then the car IS falling inwards (but we don't usually use the word "falling" for that). – Andrew Steane Sep 01 '21 at 14:59
  • @UNDEFINED: See my edit to the second paragraph. – Michael Seifert Sep 01 '21 at 16:12
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I think the confusion is more general. About what those two forces are:

Centripetal

When a truck is going around a curve at constant speed, its velocity is changing. Velocity is speed and direction. Therefore direction changing... is velocity changing. Changing velocity is acceleration.

So, it takes acceleration to move along a curve. By $F=ma$, that takes force. That’s called centripetal force, the force to keep something turning (and eventually revolving around a center-point ). Centripetal force points in the direction of velocity change: toward the center. The force needed to keep the truck turning is toward the center of curvature. The force comes from friction. That’s why if it was slippery the truck would slide outward, away from that center of revolution, from the center of the curve. If slippery, there’d be insufficient centripetal force to keep it turning. That’s all from a still frame.

Centrifugal

If you’re in the truck, you feel a force pulling you away from the center (relative to the truck), as if there is extra gravity. The truck is an “inertial reference frame” and is accelerating (turning). The apparent force felt by things in the revolving frame is called centrifugal force and it is directly outward. So if something in the frame of the truck is slung outward, THAT force slinging it.. is centrigul force.

Al Brown
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  • i got your point . i had another doubt, can component of any force be considered as a centripetal force? – UNDEFINED Sep 02 '21 at 04:39
  • @UNDEFINED Centripetal forces are only forces the curve the trajectory of something, which as mentioned is a type of acceleration, hence needing a force ti make it happen (the centripetal force). Think about them from a still frame. You can have other types of acceleration not just curving a trajectory. Like plain old increasing its speed (which unlike velocity is not a vector). And you can have other types of inertial frames. The first step is to really understand inertial frames, maybe my answer here will help w that: https://physics.stackexchange.com/a/659242/307354 – Al Brown Sep 02 '21 at 05:37
  • Try that again: “Centripetal forces are only forces that curve the trajectory of something, which..” The rest is ok. Speed just means the magnitude of velocity. – Al Brown Sep 04 '21 at 07:44