Can you fall in a Gravitron centrifuge ride?

Question

I went on a Gravitron ride with my 5 year old son. He became "hysterical" with fear and started pushing himself off the wall. I my arm across his body trying to keep/push him back as he was actually somehow able (adrenaline I guess) to separate most all of himself from the wall pushing away from it with his hands and feet. I was petrified that if he succeeded, that he would fall.

It was years ago and he recently asked his high school physics teacher about this who responded that it would have been impossible for him to break/fall away from the forces of the ride. I don't understand- would he not have "broken" the centrifugal and centripetal forces if he actually fully peeled himself away from the wall - becoming 'independent' of the ride? Can you explain this to me, please?

Answer 1

If the ride is set up the same as this video, then no, I do not believe your son was in any danger.

The centrifugal force keeping him pinned to the wall was due to his own motion (imparted by the friction of the ride when it spun up originally), and not dependent on contact with the wall. The effect is the same as if there were a force of gravity pointing outwards. So he could no more fall off the slanted wall than he could "fall off" the normal flat ground by doing a pushup on the ground.

I read that a typical centrifugal acceleration is perhaps $3$ to $4$ $ \text g$ on that ride. So while the ride is spinning, the total force of gravity the riders experience is

$$ \mathrm{arctan} \left( \frac{1}{3} \right) = 18.4°$$

downward from from the horizontal, instead of the normal vertical downward.

With that said, leaning or jumping away while the ride is ending might be dangerous. And a further caveat, I am not the engineer who designed the ride and am not even positive which ride you are referring to, so obviously do not take this as assurance to do anything in real life without consulting the ride designers and/or owners.

Answer 2

The centrifugal pseudo force is a result of the fact that an object traveling with no acceleration in an inertial frame will have acceleration relative to a rotating coordinate system. This acceleration, and hence pseudo force, is entirely due to the coordinate system, and not anything physical acting on the object, so your son will have this pseudo force acting on him regardless of whether he is in physical contact with the wall. If he had thrown a ball "upwards", the ball would have fallen back "down", even though it was not in contact with your son or the wall.

However, the strength of the pseudo force is proportional to the distance from the axis of rotation, so when your son moved away from the wall, he did decrease the force somewhat (and also experience Coriolis force pushing him sideways). This probably wasn't significant, though. For instance, if the ride was 10m across and he moved 1m away from the wall, then he decreased the force by 10%.

Another factor is that the centrifugal pseudo force was in addition to, not a replacement of, gravity. He still had gravity pulling him down, and the reason he didn't fall is that the normal force between him and the wall created friction that was stronger than gravity. If his movements caused him to change the amount of friction, that would theoretically be a mechanism to make him fall.

So as for the question of "Can someone fall in a Gravitron type ride?", I don't know whether any ride is constructed in such a way as to make it possible, but from a physics perspective, it certainly would be possible for a ride to be built in such a way that it is possible. If there was just barely enough friction to keep people in place when they're lying down, and they moved around in such a way as to decrease the friction, they could fall.