Understanding Earth's Rotation: Impact on Reference Frames

[koolraj09]

Urgent-About reference frames!

Hi guy's.
I thought about this for quite a while but could not convince myself to believe it. I may be wrong somewhere but still any help would be greatly appreciated.
The question:
Now the Earth rotates at a speed of 7.29*e^-5 rad/sec.,so that any point on it's surface moves a linear distance of 465m approx. in 1sec.(considering tangential velocity of earth). Now that suppose we are in a helicopter which is in air above the ground (earth's atmosphere) and the helicopter has zero absolute velocity(indirectly is it inertial frame of reference). Now, if we see Earth rotating from the helicopter we would see any point on it(earth) covers a distance of 465 m in 1sec.(i made the helicopter stationary while the Earth is still moving) So we do not need the helicopter to travel here n there but to stand still in air while we reach our destination only because of the Earth's rotation. This seems contradictory to our real world experience??
This means that if we jump in air for 1sec. then by that time Earth would have moved by 465m. but still we land on the same spot instead of landing 465m sideways? rather than going 465m left or right.

 

[phyzguy]

Bear in mind your tangential velocity is really only true at the equator, as you move toward the pole your tangential velocity will decrease proportional to cos(latitude).

However, that isn't really your problem. Suppose you jump up at the equator. The Earth beneath your feet is moving tangentially at 465 m/s, as you said. But you are also moving tangentially at 465 m/s. You don't lose this velocity just because you jumped in the air. So you and the Earth continue to move sideways at 465 m/s while you are in the air, and you land at the same point on the Earth that you jumped up from.

 

[Janus]

Also, for the same reason Phyzguy gave, the Earth's atmosphere (for the most part) shares the Earth's rotation. To "stand still" while the Earth turns under you would require you to fight 1674 kph winds at the Equator.

 

[koolraj09]

Thanks for Ur replies.

 

[koolraj09]

hi again. does this mean that an airplane always rotates with the earth?? i want to ask that what is the nature of relative motion of the plane?

 

[koolraj09]

Ok. But I still have a question.We know that the Earth rotates from east to west. So if we want to travel from west to east we would require first to overcome the Earth's rotation first and then impart a velocity greater than 465m/s so that we can go eastwards. Am I right?
and again does an airplane always rotates with the Earth or it goes against the Earth's rotation.
EDIT: I presume that the atmosphere of Earth also rotates from east to west. So while going from east to west we would require you to fight 1674 kph winds at the Equator.

 

[Doc Al]

Ok. But I still have a question.We know that the Earth rotates from east to west. So if we want to travel from west to east we would require first to overcome the Earth's rotation first and then impart a velocity greater than 465m/s so that we can go eastwards. Am I right?

No. First, the Earth spins in a counter-clockwise direction as viewed from above the north pole. That means it rotates toward the east. But you are moving along with the earth, so you don't need any minimum speed to go in any direction you like. You can easily walk in the opposite direction to the Earth's rotation, right?

and again does an airplane always rotates with the Earth or it goes against the Earth's rotation.

Planes can fly in any direction, if that's what you're asking. As has been explained, the atmosphere moves with the earth.

EDIT: I presume that the atmosphere of Earth also rotates from east to west. So while going from east to west we would require you to fight 1674 kph winds at the Equator.

No. There's no 1674 kph wind to fight.

Janus' point was that if you wanted to not go along with the Earth's rotation (and just remain fixed in space above the Earth's rotating surface) then you'd have to fight those winds--because the atmosphere moves with the earth.

 

[vandegg]

Everything on the Earth including you and the helicopter is rotating with the earth. To go from west to east just requires you to move west to east as if nothing else was moving. The reason we talk about reference frames and whatnot is because if everything is moving uniformly with the same velocity then it is mathematically identical to nothing moving.

 

[koolraj09]

Is the speed of sound 340m/s measured w.r.t earth? because we can already see that tangential velocity of Earth is 465m/s which means supersonic.

 

[Doc Al]

Is the speed of sound 340m/s measured w.r.t earth?

Yes. The speed of sound is with respect to the air, which moves with the earth. (Roughly speaking.)

because we can already see that tangential velocity of Earth is 465m/s which means supersonic.

So? The Earth is also moving with respect to the sun a lot faster than that.

 

[koolraj09]

Sorry ehh..but I'm still confused. Again consider an airplane. I think when it takes off from ground Earth has already imparted a horizontal velocity of 465m/s. So the airplane must have a velocity greater than 465m/s to take off and reach it's destination,right? So even a small airplane "may" be supersonic..? Or for that matter a simple stone thrown upwards from Earth has a velocity greater than 465m/s.

 

[Doc Al]

Sorry ehh..but I'm still confused. Again consider an airplane. I think when it takes off from ground Earth has already imparted a horizontal velocity of 465m/s.

Not with respect to the earth, which is all that matters. With respect to some 'fixed point' in space (not rotating with the earth), the earth, the plane, the air, and you all have a horizontal speed of 465 m/s. So?

So the airplane must have a velocity greater than 465m/s to take off and reach it's destination,right?

Nope. It's already moving at the speed of the earth.

So even a small airplane "may" be supersonic..? Or for that matter a simple stone thrown upwards from Earth has a velocity greater than 465m/s.

Not with respect to the earth, which is what you care about. You and the stone move together.

You are moving much faster than 465 m/s with respect to the sun. Do you think that effects the way planes fly or how stones move when thrown?