newtonian mechanics - Is centripetal acceleration mandatory for circular motion?

If we consider a case where a closed circular wall is present, and inside the boundary, just adjacent to the inner wall, two particles are placed touching the surface of inner boundary such that the distance between both particles tends to 0. Particle A and B have identical masses, shapes and physical properties. Particle B applies a constant force on particle A and particle B is in uniform circular motion. Thus, particle A also moves in a circle. And here, centripetal force is not required to make particle A move in a circle.

What's going on?

Answer

Let me try to add a missing intuitive piece in the explanation to the discussion to @Gert's answer of why there must always be radial acceleration for any circular motion.

Remember what acceleration is: Change in velocity. $\vec a=d\vec v/dt$. More mathematically it is change in the velocity vector.

If velocity is changed - either magnetude or direction - then we define this rate of change as acceleration.

• If the velocity magnetude is changed, then acceleration is pointing in the same direction as the velocity (and it goes faster or slower). We call this tangential acceleration.


• If the velocity direction is changed, then acceleration is pointing to the side and not parallel to the velocity direction. If it is exactly perpendicular to the direction we call it radial acceleration.

Now imagine what happens if an object has no tangential and only radial acceleration. Then it keeps its magnitude (so the speed doesn't change) and only changes direction. Thinking more about this it should be clear that such a situation is a circular motion. If there both is tangential and radial acceleration, then the we have an elliptical motion.

Naturally, for any path that is not straight, there must be a change of the velocity direction. And we call such a change acceleration - for a circular motion that acceleration happens to be perpendicular and towards the center of the circular path.

Any forces that act on a particle in a circular motion therefor must result in such a sideways acceleration. If they do not, then the motion cannot be circular because of the above explanation.