So I'm having a bit of struggle understanding the origin of the centripetal force. Is the centripetal force a pseudo force? Somebody told me that both the centrifugal and the centripetal forces are pseudo forces. I get it for the centrifugal one, its acceleration comes from the change of direction every dt units of time of the velocity vector. But then, it seems to me that the centripetal force is quite real. The centripetal force being the one that cancels the centrifugal, is it the tension of a rope or the reaction of a wall (depending of the motion you re imagining)? Well Im a bit confused, thank you for reading and have a nice day!
Centripetal force is not a force in itself, it is the name given to any center seeking force which possesses the ability to move a body in a circular path. It's NOT a pseudo-force, because this force is recorded and measured from the ground and not a non-inertial frame. To understand this look at the instance of a body being rotated in a circle by a taut string. In this case , the string provides tension which ACTS as the centripetal force, and thus the tension can be equated to the general formula of a centripetal force ( mv^2/r) . Remember the net-force( acting towards the center) which aids a particle in performing circular motion, is the centripetal force. Thus while making an FBD you don't explicitly draw the centripetal force, you just take the net-resultant force towards the center and call it the centripetal force. It's just a name/label. On the other hand The centri-fugal force is pseudo as we record it from the accelerated frame of the block, which is non-inertial. A pseudo-force is used only when we want an object being observed from the non-inertial frame, to obey Newton's laws w.r.t the frame.
Generations of students have been confused by the meaning of fictitious forces in non-inertial frames, but there is a very simple way to explain what a fictitious force is.
We start by reminding ourselves of Newton's first law:
Newton's First Law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
Now suppose we lay out some coordinates with you at the origin and me standing still due North of you:
You observe me to remain at rest just as Newton's first law describes, so we know there isn't any force acting on me. Now suppose you start rotating anticlockwise. Now let's have a look at what you see:
In your (rotating) frame I no longer remain at rest, and indeed I'm not even in uniform motion in a straight line, so Newton's first law tells you that there must be a force acting on me to make me move in a circle.
And this is what we mean by a fictitious force. We know there can't be any forces acting because all that's changed is you have started rotating. But it looks to you as if there is some centripetal force that is pulling me towards you. This is the fictitious force.
Note that I've set up the situation so that I am stationary while it's you that is rotating. Typical descriptions of the situation involve stones being whirled around on strings while the observer in the centre is stationary. The trouble with this is that there are real forces acting, i.e. the tension in the string, and I think this makes it harder to understand what a fictitious force is. The centripetal force is real because it's the force the string exerts on the stone to pull it inwards. The centrifugal force is also real because it's the force the string exerts on the central pivot to pull it outwards.
The centrifugal force (causing a planet to leave its orbit and fly away) is a pseudo force. This is because it is not so much a force unto itself but a consequence of the laws of classical mechanics, gravity and electrodynamics. In short, a number of axioms about matter forbids it from being able to orbit stably unless a real force - the centripetal force brought about by gravity, on our example planet -keeps it there.
Centrifugal force is a pseudo-force because no one fundamental force alone is responsible for it. Centripetal force is a real force because it is directly caused by the fundamental forces attracting matter.
The centrifugal force itself does not exist. What you feel when travelling in a circle around something is the centripetal force, which is needed to counteract the orbiting body's inertia. Inertia wants it to keep flying in a straight line, tangential to the orbit. The centripetal force forces it to stay in orbit. Without that force, the body in orbit would simple obey inertia and fly away in the direction that it is going, i.e. tangential to the circle. This is valid, regardless of whether the centripetal force is caused by a string, or by the earth's gravity forcing the moon to stay in orbit.
If you spin a rock around on a string, and suddenly cut the string (the centripetal force), the rock does not fly directly away from you, as would be expected if the centrifugal force were real. Instead, it flies away tangential to the circle. People who use old fashioned slings (e.g. the Bible's David) know that they have to let go when the rock is 90 degrees from the target, not when it is lined up with the target.