Coriolis Force & Rotating Body Problem

[Jimmy87]

Homework Statement

Coriolis Force - Explain how the following situations would appear in both the inertial and non-inertial reference frames. Assume the inertial frame to be a view from above.

Situation 1 - a ball is thrown from the centre of a merry-go-round which is rotating counter-clockwise to a person on the outside.

Situation 2 - the person from the centre now walks to the person on the edge.

Homework Equations

None given.

The Attempt at a Solution

Situation 1 I think I can explain. The view from above (inertial) will see the ball go in a straight line. From the non inertial frame it would appear to curve to the right since the person on the outside is moving faster than the person from the centre.

Situation 2 I am really struggling with. I know it's different because we are dealing with a person in contact with the merry-go-round. From reading around I think the inertial view from above would see the person walk in a curved path but I can't explain why. I thought that only non-inertial frames see a curved path. I know that as he walks out he will be stepping onto faster and faster rotating ground but so long as he doesn't slip wouldn't he just walk in a straight line?

Thank you for any help as I am struggling with this!

 

[Simon Bridge]

Good effort. Focussing questions:
S1. the non-inertial observer is standing on the outside of the merry-go-round?
S2. consider - the center person is walking in a straight line in the rotating frame ... what does that look like from above? (The person on the edge is stationary in the rotating frame - what path do they trace out in the inertial frame?)

 

[Jimmy87]

Good effort. Focussing questions:
S1. the non-inertial observer is standing on the outside of the merry-go-round?
S2. consider - the center person is walking in a straight line in the rotating frame ... what does that look like from above? (The person on the edge is stationary in the rotating frame - what path do they trace out in the inertial frame?)

Thanks. I'm still confused about S2. In helping me to visualize it (which I'm really struggling with) imagine there is a straight line painted on the merry-go-round from the center to the person on the outside. If the person in the center walks along that line then would they both see this as walking in a straight line? I'm still not sure what the inertial frame sees as wouldn't they still see the man from the center walking along this straight line?

 

[Simon Bridge]

Thanks. I'm still confused about S2. In helping me to visualize it (which I'm really struggling with) imagine there is a straight line painted on the merry-go-round from the center to the person on the outside. If the person in the center walks along that line then would they both see this as walking in a straight line? I'm still not sure what the inertial frame sees as wouldn't they still see the man from the center walking along this straight line?

That's not the way to visualize it - because, to the overhead observer, the long line is rotating. Thus the rotation of the line adds another component to the persons motion.

Consider: imagine the person stood still on the line - then the overhead observer would see the person go in a circle right?

 

[Jimmy87]

That's not the way to visualize it - because, to the overhead observer, the long line is rotating. Thus the rotation of the line adds another component to the persons motion.

Consider: imagine the person stood still on the line - then the overhead observer would see the person go in a circle right?

OK I think I see now, I think I was looking into it too much. I just managed to find this link (http://en.citizendium.org/wiki/Inertial_forces#Crossing_a_carousel). So the inertial observer sees a spiral path because the carousel is rotating from an inertial perspective. Where does the Coriolis force come in and which reference frame needs it to explain their observations?

 

[Simon Bridge]

The coriolis force is like the centrifugal force - it is needed in the non-inertial reference frame.
If you ever get the chance to walk about on a big rotating platform you should do so - you feel like there is an invisible hand pushing you about and throwing off your balance. To walk in a straight line you have to fight it.

The inertial observer goes, "Well of course the path is a spiral, the target they want to walk towards is constantly changing position!"

 

[Jimmy87]

The coriolis force is like the centrifugal force - it is needed in the non-inertial reference frame.
If you ever get the chance to walk about on a big rotating platform you should do so - you feel like there is an invisible hand pushing you about and throwing off your balance. To walk in a straight line you have to fight it.

The inertial observer goes, "Well of course the path is a spiral, the target they want to walk towards is constantly changing position!"

Thank you, that is making a lot more sense now. Just one final questions if you would be so kind. The wiki link I put in says that the non-inertial reference frame sees straight line motion with no net forces but the inertial frame sees no such thing (namely a spiral instead). It then says that the inertial frame sees two forces; centripetal force and a force perpendicular to the radius which is proportional to the speed of the walker. The equivalent forces in the non-inertial frame are centrifugal and Coriolis forces. But it then says that this still doesn't explain straight line motion in the rotating frame so it says that the Coriolis and centrifugal forces must be exactly countered in the rotating frame for the inertial observer to agree. What are these specific forces that are being applied to counter the centrifugal and centripetal?

 

[Simon Bridge]

In the rotating frame, you walk a straight line by applying a force (your feet on the ground) to oppose the pseudo-forces that keep trying to push you off-line. Thus no net force.

Your book kinda has it backwards though - the existence of the pseudo-forces is deduced from the need to exert an applied force of your own to keep going in a straight line.

It's like if you are in a closed box, a railway carriage say, and you see that a weight suspended from the ceiling hangs at an angle to the vertical, you would deduce that there is some force other than gravity present causing that effect. However, it could be that the box has uniform acceleration in a straight line...