Problem with a common Physics question.

[vcapital2000]

Calculate how long would a day be if the Earth were rotating so fast that objects at the equator were apparently weightless?

 

This is a question of posed and asked for a solution. Perhaps it is semantics or the way I am viewing weightless incorrectly, I have a problem with this question itself. Weight is commonly defined as the force on the object due to gravity.

 

Now the solution to the problem is the earth would need to rotate approximately 17x faster to achieve weightlessness. Where the spin of the earth would be so fast it would cancel out the pull of gravitational forces.

 

My question is this. Isn't this just buoyancy and not weightlessness? If I were to dive into the ocean and reached a certain point in buoyancy I would be simulating weightlessness but never achieving it. My weight has never changed and the ocean is slightly heavier for me being in it.

 

The other problem I have with this question is that everyone seems to believe that once the earth rotated at such an extreme speed that objects would simply fly off into space.

 

If I were to fly from the North Pole to the Equator then jumped out I would still fall to earth regardless of rotation speed of Earth. My weight never changes what changes is once I impact to Earth. Now wouldn't objects simply skip across the Earth at this rotation since gravity would still constantly be pulling them back?

[Strange]

 

My question is this. Isn't this just buoyancy and not weightlessness?

 

It isn't buoyancy, because that is a reduction in weight caused by displacing a fluid.

 

 

My weight has never changed

 

Are you confusing mass and weight? If you were to stand on bathroom scales underwater, you would weight less. But your mass would be unchanged.

 

 

Now wouldn't objects simply skip across the Earth at this rotation since gravity would still constantly be pulling them back?

 

The question assumes that the objects are rotating at the same speed. It isn't meant to be physically realistic. You may be overthinking it.

[pzkpfw]

The question says "apparently".

[Janus]

The other problem I have with this question is that everyone seems to believe that once the earth rotated at such an extreme speed that objects would simply fly off into space.

 

If I were to fly from the North Pole to the Equator then jumped out I would still fall to earth regardless of rotation speed of Earth. My weight never changes what changes is once I impact to Earth. Now wouldn't objects simply skip across the Earth at this rotation since gravity would still constantly be pulling them back?

Objects at the equator would be traveling at orbital speed. They essentially be orbiting the Earth at the same speed that the Earth rotated and would be in geostationary orbits. A long as they don't try and change their speed with respect to the Earth, they will remain so.

 

If you fly from the North pole to Equator, and assuming the atmosphere rotates with the Earth, you and your plane will also be moving at orbital speed upon reaching the Equator. But since you will be a little further from the center of the Earth than the people on the surface, you will actually be traveling faster than orbital speed at your altitude. You will actually climb away from the Earth. You will try to enter an elliptical orbit with a perigee at the altitude at which you jumped out. However, the Earth's atmosphere won't quite let you. As you climb to the apogee of your new orbit, you will tend to slow down with respect to the Earth's rotation. Air drag won't quite let you slow down as much as you normally would and, as a result you'll always be orbiting a bit faster than you should and this will result in your continuing to climb away from the Earth until you reach a point where the atmosphere has thinned to point that the drag becomes insignificant.

 

For people on the surface, their attempts to move relative to the surface would create some interesting effects. (for example, if you tried to go forward in the same direction as the Earth's rotation, you would find yourself lifting away from the surface, at first you also travel in the intended direction relative to the surface, but as you climbed you would slow and drift backwards. rt some point behind where you started you would start moving forward again and falling back down, but you will end up touching the surface behind where you started (actually, as above, atmospheric drag will just stop you shy of touching down again.)