Inertial problem:is the helicopter still moving with the speed of the rotating earth?

1. Oct 29, 2004

tmwong

a helicopter flies up straightly perpendicular to an "X" marked on a floor. then, the helicopter keep static in the air when it has reached 10m from the floor. after 5 hours, will the "X" still remain right on the floor below the helicopter?

2. Oct 29, 2004

reilly

What could make it otherwise?
Regards,
Reilly Atkinson

3. Oct 29, 2004

tmwong

actually, my point is that will the X "moves" away as the earth is rotating after 5 hours?
for example, the earth is rotating with the speed 1km/s(just an example coz i dunno what's the actual speed). will the helicopter remain the speed of 1km/s in the direction of the rotation of the earth while it's floating staticly on the sky. it's because newton's nertial law tells us that the objects inside the same reference frame will have the same speed with the reference frame if no other force is applied to the objects inside. in my question before, the earth is the reference frame and it's moving in the speed of 1km/s and the helicopter is the object inside the reference frame. so, is the helicopter still have the same speed with the earth, which is 1km/s, after 5 hours? if yes, the X will remain 90 degree below of the helicopter.

4. Oct 29, 2004

dextercioby

that's funny...

If Newton's law would not apply,it would be a great problem (actaully a fatal one) for those athletes in the high jump discipline.They would definitely be crushed by the stadium approaching them at 465 m/s (at the equator)... :rofl: That's the first example that crossed my mind.Other even more sadistic could be imagined.

5. Oct 29, 2004

BobG

I think it was Isaac Asimov that wrote a short story about a scientist, who was very smart but very poor, that found a way to bring any object to a complete stop instantaneously. A rival scientist, less smart, but more famous and rich, publicly ridiculed the poor scientist's theory. The two scientists often challenged each other to billiards, so the poor scientist invited the famous scientist to a demonstration of the first operational 'anti-momentum machine'. The poor scientist demonstrated how his anti-momentum machine worked by shooting a pool ball into the anti-momentum field.

If you add the rotation of the Earth, the Earth's motion around the Sun, the Solar System's motion about the center of the Milky Way, the Milky Way's motion, etc., etc., it's amazing how fast all those velocities add up.

I liked that story almost as much his story about the poor soccer referee who made a bad game deciding call against the home team. 100,000 mirror weilding fans focusing their ire into one united effort can really make a referee's blood boil. I referee soccer and always use that story to comfort comrades who've just endured the fury of a critical blown call.

6. Oct 29, 2004

Gonzolo

Let's examine two cases :

1. As the helicopter gains in altitude, it keeps its inertia in the horizontal direction, as does the air which supports it, so if he is above the equator, would stay right a top the x. (Of course, the pilot has to have the x as a reference over which to fly, but what I mean is that he will not have to make corrections if he is near the equator. I believe "near the equator" includes most of the industrial world : up to 60 or 70 degrees in latitude.)

2. If he is flying above the north pole, he will have to yaw, because the earth and atmosphere will tend to spin under and around him.

So if he is "near" the north pole, then yes, the pilot will have to make corrections to stay over the x. The perceived force is exactly what is called the Coriolis effect and is entirely compatible with all that Newton has to say. The amount of corrections depends on the helicopter's horizontal speed and latitude (+ distance and time of travel), and it does have to be accounted for in self-guided systems or by visual pilots (perhaps unkowingly when flying visual). Even some advanced training simulators (for helicopters and planes) take it into account.

Last edited by a moderator: Oct 29, 2004
7. Oct 29, 2004

BobG

The helicopter did not maintain a constant speed. It accelerated in order to raise it's height. Even if it is only pushing in a radial direction (directly away from the center of the Earth), the atmosphere is pushing in the direction of the Earth's rotation and giving the helicopter some tangential acceleration.

However, if the Earth were a vacuum, a push strictly in the radial direction with no tangential component would cause the object to fall behind the Earth's rotation. You add energy, you increase the size of an object's orbit, regardless of how you add the energy - in other words, if a geosysnchronous satellite is accelerated in the same direction of the Earth's rotation instead of radially, it will still increase the size of the orbit and its angular velocity will still fall behind the Earth's angular velocity.

8. Oct 29, 2004

Gonzolo

There is however an initial tangential component of speed, whether atmosphere or vacuum. It is the reason for 2D-directionnal symmetry in our daily lives (high jump, golf etc.).

9. Oct 30, 2004

tmwong

if the helicopter is not flying in the vacuum, the air or the wind will become the friction forces to the helicopter. then, the inertial tangential component of the helicopter would be effected by these frictions. with this reason, i suppose that the pilot would see the X "moving" away slowly from the below of his helicopter.