Maglev Train and Earth's Rotation

[DBirk]

Homework Statement

Will a maglev train beginning at rest slowly drift or accelerate due to the rotation of the earth?

Homework Equations

The Attempt at a Solution

The Earth is a rotating reference frame, with points on the equator moving at approximately 1000 miles per hour. If the maglev is not coupled in any way to the Earth (via friction), I would expect that the Earth would begin to move underneath the train, and the train would appear to move in that reference frame. Ultimately, the train would continue to accelerate until it reached a maximum speed, limited by wind resistance.
I understand that once moving it will become subject to Coriolis acceleration, but I am interested in the question of whether or not it will go from rest to moving at all.

 

[Doc Al]

What's the initial speed of the train with respect to the earth?

 

[DBirk]

It begins at rest. Question is, will it ever begin to move, or will it remain at rest?

 

[Doc Al]

It's at rest with respect to the earth, which means it's moving as fast as the Earth is. Why should its speed change?

 

[DBirk]

Well, that's my confusion. If the Earth is a truly rotating reference frame, it moves with respect to a reference frame at rest. So, the Earth has imparted an initial speed of 1000 mph to the train with respect to the non-moving reference frame. But then the Earth no longer influences the train as it is frictionless, so I would expect the train to decelerate in the Earth's reference frame and approach rest in the non-moving reference frame.

 

[Doc Al]

Forget the train for a minute. Say you were sitting on a frictionless ice-covered pond. You're at rest, thus moving with the earth. Would you expect that you'd start to move faster and faster?

 

[DBirk]

So you are suggesting that a body in motion tends to stay in motion. i.e. there are no forces acting on the train (or me on the pond), so I will keep right on moving with the earth. I can see that.
Consider for a second coriolis acceleration. If you fire a projectile a long distance, the Earth spins underneath it, so it appears the the projectile is moving with respect to the earth. Would this effect not then also affect a body at rest if it is frictionless?

 

[Doc Al]

Consider for a second coriolis acceleration. If you fire a projectile a long distance, the Earth spins underneath it, so it appears the the projectile is moving with respect to the earth. Would this effect not then also affect a body at rest if it is frictionless?

No. There's no coriolis force for a non-moving body. (Non-moving with respect to the rotating frame.)