Posted: Apr 14, 2015 3:00 am
Jerome Da Gnome wrote:Am I too dumb to understand, or are you too dumb to explain?
In your last post you appear to confuse "angle" with "angular momentum", which is what 8th-9th grade stuff?
As I suggested you seem to be lacking some fairly basic and key education that might allow you to access the answers you've been given, but you aren't displaying much of a willingness to learn, so I'm not super keen to spend a lot of time on it, not being a high school physics teacher.
In simple terms there's a fundamental concept in physics called an "inertial frame" - which is simply a frame of reference (i.e. a co-ordinate system) in which there are no "fictitious" forces such as centrifugal force. This means that basic laws of physics hold true in any such frame.
Now, in such a frame there are certain important physical quantities such as momentum (given by p=mv) and angular momentum (given by L=r X p, where X denotes the "cross product" not multiplication) that are preserved. The frame centred on the Earth and rotating with it is not an inertial frame because the Earth is rotating, which leads to measurable "fictitious" forces like centrifugal force, which means you can measure things like the Coriolis effect (e.g. deflection of ballistic projectiles at latitude).
What this means is that any outward radial motion from the centre of the Earth (i.e. jumping upwards by exertion of a single force in the "upwards" or radial direction) is going to lead to a reduction in angular speed due to conservation of angular momentum.
However, the size of this change is small and the Earth drags its atmosphere along with it, so as you gain altitude you will be buffeted by winds which will change your angular momentum and give you approximately the same angular speed - i.e. you will continue to go pretty much "straight up" as long as you're inside the atmosphere. After that the effect will be more and more noticeable and the Earth will appear to rotate more and more under you as you get further and further away.
The answer is thus that there is no single point at which the system discretely changes from you rotating with the Earth so the point of departure is "straight down" to the point of departure rotating under you. Instead there's a continuous change in relative velocity that will start to become apparent as the atmosphere thins.
This is very easily seen by simply learning the definitions of angular speed and angular momentum and noting that angular speed is a decreasing function of radius when angular momentum is a fixed value.