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| A 'simple' Physics postulation... |
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| GlennSprigg:
In reference to JUST the local surface of the Earth where you stand, (NOT the solar system, galaxy etc!!)... If you were able to throw an object 'exactly' vertical, such that it came back to you due to gravity, did the object ever 'Stop' at it's apex?? Obviously, it can't have, even for 1/1000000000-th of a second, as that would defy the laws of physics. So it is only ever going up, or coming down. Without stopping!!? :phew: |
| Brumby:
Define "Stop". |
| retiredfeline:
Maybe you've discovered oneZ's Arrow paradox. :-DD |
| Ian.M:
You'd need to go to the Earth's North or South pole to conduct your experiment, otherwise, as you throw it upwards it will drift off to the West, due to the Earth's rotation. (As the tangential velocity required to remain 'stationary' with respect to a rotating frame of reference is proportional to the rate of rotation and the radius from the axis of rotation, it doesn't have enough tangential velocity to maintain its angular position at a greater radius from the center of the Earth.) Therefore if you throw an object so that it lands exactly where thrown from anywhere other than the poles on the Earth's surface, to do so you *CAN'T* thow it vertically, you have to tilt your throw ever so slightly East to give it the extra angular velocity required. Its trajectory will therefore be a tall extremely skinny* loop, west-bound at the top, and, in flight, it will *NEVER* have zero velocity with respect to the point it was thrown from, and lands at. At the poles, for an infinitesimal instant at the apex of its vertical trajectory, it has zero velocity. Its speed with respect to the surface is a continuous function so how else is it going to get from positive (distance increasing = ascending) to negative (distance decreasing = descending) without going through zero speed? * The tangential velocity difference over 100m height difference at the equator is (if I've done the maths right) only 45um/sec, so is normally absolutely imperceptible. --- Quote from: Brumby on July 09, 2021, 11:09:34 am ---Define "Stop". --- End quote --- *EXACTLY* *THIS* Velocity and acceleration both zero for a non-zero time interval (i.e. Physics: 'At rest') would probably be a reasonable definition. |
| Brumby:
Aside from the polar conversation (which is valid) it is this which contains the key elements of the answer: --- Quote from: Ian.M on July 09, 2021, 01:50:57 pm ---...... for an infinitesimal instant at the apex of its vertical trajectory, it has zero velocity. --- End quote --- The word "instant" is key here. The OP is considering a period of time - which cannot deliver a zero value.... Unless you take that period to be equally before and after reaching the apex in which time the net velocity will be zero. (But, I don't think the OP will be happy with that.) However - this statement not only allows, but requires a zero velocity at a point in time: --- Quote ---Its speed with respect to the surface is a continuous function so how else is it going to get from positive (distance increasing = ascending) to negative (distance decreasing = descending) without going through zero speed? --- End quote --- |
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