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When the marble is viewed from with respect to the ground, it experiences a net inward acceleration, and hence force. However, when the marble is displaced slightly, it moves towards the edge. Why? My first answer would be centrifugal force, but isn't it fictitious?

EDIT: The marble isn't the center of the conversation here. It's the outward force. The marble and the merry-go-round can be substituted with just about anything. A car on a bend, a child being spun around by someone or a centrifuge. My question is simply, why does any of these "things" get pushed outwards. A simple answer would be centrifugal force. But isn't that fictitious? The reason why I asked about the marble and merry-go-round is because of a thought experiment involving the two in Physics by Resnick and Haliday.

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marked as duplicate by sammy gerbil, Yashas, Kyle Kanos, John Rennie newtonian-mechanics Jun 5 '17 at 15:26

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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Imagine first an object with perfect circular motion (on the left in the image below) - a ball on the end of a rod for example. It starts with some initial velocity (green line), the radial acceleration (red line) varies this velocity such that it continues along a circular path.

Some none perfect transfer of the force - your marble on a merry go round, for example - would experience the same radial acceleration but not sufficient that it removes all component of the objects velocity in one direction.

In the image below the ball starts with it's velocity entirely in the $y$ direction and then, at the top, the ball has it's velocity entirely in the $x$ on the left hand side but the right still has some component in the $y$ - hence the ball moves a little in the $y$ direction too.

Circular motion

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  • $\begingroup$ Assuming that the merry-go-round is a undergoing perfect circular motion (along with everything placed on it). Would the marble then be pushed to the edge? Or would every point be a point of equilibrium? $\endgroup$ – abhijeetviswa Jun 4 '17 at 17:49
  • $\begingroup$ The marble will continue rolling out unless there is some radial dependent force acting inwards (if the merry-go-round was curved upwards more the further you went out, for example, the marble would find an equilibrium point) but as it is it won't find an equilibrium point. $\endgroup$ – Lio Elbammalf Jun 4 '17 at 19:57
  • $\begingroup$ And what is the reason for this radial outward force that pushes the marble outwards? (Assuming perfect circular motion and not what you described in your answer) By the way the, the marble and the merry-go-round can be substituted with anything. A car on a bend, a child being spun around by someone or a centrifuge. My question is simply, why does any of these "things" get pushed outwards. A simple answer would be centrifugal force. But isn't that ficticious? $\endgroup$ – abhijeetviswa Jun 5 '17 at 5:12
  • $\begingroup$ @Abhi2011 In perfect circular motion we see the ball at a constant radius, we need a constant force inwards to keep it this way. In the rotating frame this force is then seen as the norm (ie 0 force radially) so if it is taken away we imagine a force radially outwards in the rotating frame. It is fictitious. $\endgroup$ – Lio Elbammalf Jun 6 '17 at 7:18
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Objects are not pushed outwards relative to the ground. There is no outward force in this frame of reference. If the object is suddenly released (as in a catapult) it flies off at a tangent wrt the ground, with the velocity it had at the instant of release (Newton's 1st Law). This motion requires no force. This velocity is perpendicular to the initial radius, so the object will eventually cross the circumference of the circle.

In the frame of reference of the rotating platform, the object gets further from the centre, but it also veers off to one side tangentially. (Looking down on a platform rotating anti-clockwise, the object veers clockwise.) The radial component of this motion is attributed to Centrifugal Force, while the tangential component is attributed to the Coriolis Force.

enter image description here

Source: Hyperphysics website.

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  • $\begingroup$ "In the frame of reference of the rotating platform, the object gets further from the centre, but it also veers off to one side tangentially." Veering off tangentially is the Coriolis force (explained using the velocity component) but what is the reason for the object moving outward? Pretty much what I'm asking is why does a centrifuge, rotating in a horizontal circle push stuff to the perimeter. Centrifugal force isn't the reason since it's a pseudo force. Just like Coriolis force is explained by tangential velocity, what explains the centrifugal force? $\endgroup$ – abhijeetviswa Jun 5 '17 at 16:19
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    $\begingroup$ Sorry, I don't understand why you accept that Coriolis force is explained by tangential motion but you don't accept that centrifugal force is explained by radial motion. Both Coriolis and centrifugal forces are pseudo forces : they don't exist in inertial frames of reference. $\endgroup$ – sammy gerbil Jun 5 '17 at 20:27
  • $\begingroup$ Because there is no radial motion. When I rotate a stone tied to a string in air and slowly extend the string, there was never any outward radial motion. There was only an inward radial force. $\endgroup$ – abhijeetviswa Jun 6 '17 at 3:12
  • $\begingroup$ There is radial motion on the merry-go-round : the object "moves towards the edge" as your title says. When you rotate a stone on a string, if you extend the string, you are increasing the distance from the centre. Angular momentum is conserved, so the angular velocity decreases. Relative to the original frame rotating at the initial angular velocity, the stone moves outwards (radial) and also veers to the side (tangential - because rotation rate has decreased). Centrifugal force is felt as the decrease in centripetal force. $\endgroup$ – sammy gerbil Jun 6 '17 at 8:28

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