Apparent weight on a merry-go-round

Problem

On a rotating merry-go-round you feel “squashed” outward. Explain the situation distinguishing inertial forces (rotating frame) from real forces (ground frame).

Solution

Two points of view. The sensation must be analysed by choosing the reference frame, because real and apparent forces depend on who is observing.

Ground frame (inertial). From outside, an observer at rest sees only real forces. Your body moves on a circle, so it must have centripetal acceleration $a_c = v^2/r = \omega^2 r$, directed towards the centre. The force that produces it is real: it is the wall (or the seat) of the merry-go-round pushing you towards the centre, i.e. inward: $F = m\omega^2 r \quad (\text{directed towards the centre})$ There is no real force pushing you outward.

Merry-go-round frame (rotating, non-inertial). Rotating with the merry-go-round you feel still, yet the wall presses on you. To make the accounts balance in this accelerated frame, an apparent (or inertial) force is introduced: the centrifugal force, directed outward, of magnitude $m\omega^2 r$. It corresponds to no physical interaction: it is the “price” to pay for using a non-inertial frame as though it were at rest.

The feeling of being “squashed”. What you feel is your body’s reaction: the wall pushes you towards the centre (centripetal), and by the third law you push the wall outward. The pressure on your back is real, but its cause is the push towards the centre, not an outward force.

$\ev{\text{Real: wall} \to \text{centre (centripetal)}.\ \text{``Centrifugal'' = apparent force of the rotating frame.}}$

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Topics: Dinamica Concepts: Forza centripeta · Moto circolare uniforme · Forza normale Objects: Disco rotante