Exploring Fictitious Forces in Classical Mechanics

[electricspit]

Hey!

I was wondering about the concept of fictitious forces. I'm studying classical mechanics right now and we've made our way to non-inertial reference frames.

One major problem I have is trying to understand the Coriolis force for an object falling. I understand that if an object is traveling North it will be deflected East and that if it is traveling South it will be deflected West because of the differences in speeds as it crosses across the Earth. The major problem is when you drop an object say from a very high structure (with no wind resistance, etc) it will be deflected to the East! This doesn't make any sense at all physically, unless I'm missing some major linking point.

Could anyone clarify what is actually happening? Or is this some weird thing about observing this happening from an inertial reference frame. I'm still not quite clear on that concept either.

Thanks!

 

[Nugatory]

The major problem is when you drop an object say from a very high structure (with no wind resistance, etc) it will be deflected to the East! This doesn't make any sense at all physically, unless I'm missing some major linking point.

The Earth has a radius of 6200 kilometers, and it turns on its axis once every 24 hours.

Therefore, a point on the ground at the equator moves $2\pi{R} = 38955$ km in 24 hours, for a speed of .4508 km/sec. Now consider the top of a building 1 kilometer high at the equator; the top of the building is one km further away from the center of the Earth so $R = 6201$ km and it moves 38961 km in 24 hours, or about .4509 km/sec. So an object dropped from the top of the tower will be have an eastwards speed of .4509 while the point on the ground underneath it is moving eastwards at only .4508 km/sec.

Net, the dropped object is moving east relative to the ground underneath it.

 

[jbriggs444]

The major problem is when you drop an object say from a very high structure (with no wind resistance, etc) it will be deflected to the East! This doesn't make any sense at all physically, unless I'm missing some major linking point.

Could anyone clarify what is actually happening? Or is this some weird thing about observing this happening from an inertial reference frame. I'm still not quite clear on that concept either.

The building from which you drop the object is rotating once every 23 hours and 56 minutes because it is solidly attached to the rotating earth. As judged from an inertial frame, the top of the building is moving toward the east faster than the bottom of the building. So naturally an object dropped from the top of the building will be traveling to the east when referenced against the bottom of the building.

Fictitious forces appear when trying to explain an objects apparent motion referenced against a non-inertial frame. The rotating building defines a non-inertial frame.

[Drat, Nugatory beat me to it]

 

[electricspit]

This clears everything up thank you. It makes sense now looking back on the derivation for a rotating coordinate system that a force will be apparent due to the particle moving in the rotating system just based on the change in angular momentum.

Edit: It's okay, you're both helpful. All this reference frame stuff is a fairly new concept for me so I'm just trying to get an idea of how things work. I'm still confused about observing frames vs. the actual frame the object is moving in.

 

[jbriggs444]

Edit: It's okay, you're both helpful. All this reference frame stuff is a fairly new concept for me so I'm just trying to get an idea of how things work. I'm still confused about observing frames vs. the actual frame the object is moving in.

There is no such thing as the "actual frame the object is moving in". The choice of coordinate system is arbitrary. To use your terminology, they're all "observing" frames.