I was reading about a situation in my brother’s physics textbook where a bike is riding along a curved vertical surface. It’s mentioned there that normal reaction provides the centripetal force and the bike does not fall off the wall because gravity is balanced by the friction between the bike and the surface ( if the speed is high enough). And friction depends on the normal reaction.

So my question is, what is creating the normal reaction here? My first guess was centrifugal force. But as far as I know, centrifugal force is not a real force and we need to take it into account only if our frame of reference is the bike itself. if FOR is the bike, then the bike can not have any acceleration and can be explained by centrifugal force balancing the normal reaction. But if the frame is stationary, there’s no centrifugal force. Then what’s creating a normal reaction here?


1 Answer 1


In problems like this, it is important to use Newton's 2nd Law explicitly instead of just summing forces:

$$\Sigma F = ma $$

In this case, the normal reaction force $N$ is equal to the centripetal acceleration times the mass of the moving object

$$ N = ma = m\frac{v^2}{r}$$

$v$ is the object velocity (tangent to the curved surface) and $r$ is the radius of curvature of that surface.

There is no need to invoke friction to balance gravity. Gravity may in fact be accelerating the biker downward, but this can mean reducing his upward velocity, even though the velocity is still positive upward.

As you pointed out, centrifugal force is fictitious, and is really a product of the acceleration. In rotating reference frames, you can define a centrifugal force, but as a general procedure it may be less prone to mistakes if you do not go this route.

  • $\begingroup$ But my question is about the normal reaction. Since it is a reaction, it must have an action pair. What’s the action pair that’s causing a normal reaction in this case? $\endgroup$
    – elliot
    May 25, 2022 at 11:58
  • $\begingroup$ The action/reaction pair is that the bike is pushing with $N$ force on the surface, and the surface is pushing with $N$ force on the bike. $\endgroup$
    – RC_23
    May 25, 2022 at 12:57
  • $\begingroup$ It IS necessary to look at the vertical forces too, since the bike is rotating in a horizontal plane. OP was correct in saying that friction balances the vertical weight of the bike. $\endgroup$
    – Wreckless
    May 26, 2022 at 18:42
  • $\begingroup$ Without a diagram it's basically impossible to know if we're describing the same scenario. The point I was emphasizing was that looking at the bikes free body diagram alone, there are unbalanced forces because the bike is accelerating. Nothing needs to balance gravity because gravity is unbalanced $\endgroup$
    – RC_23
    May 26, 2022 at 23:19

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