Nah, it’s just my opaquely amusing myself that all the words I kept using (deviation/displacement, distance, direction) started with ‘d’.
Yakety Sax is accompanying Bob’s back and forth circling, though.
But that’s only a by-product of the things around you – if you try to go at escape speed straight up you won’t get very far if you’re starting on the fourth floor of a six-story building. In the general case, which assumes you don’t hit anything, it doesn’t matter whether you’re heading straight away from the center of mass or almost straight at it. Either way you’re on an escape orbit.
Velocity is a vector quantity, which means it takes more than one number to describe. People have been talking as if those numbers are speed and direction, and that’s one way to do it, but another way is for the two (for 2-D motion) or three (for 3-D motion) numbers describing velocity to be speed in different, perpendicular directions. So, if you fling a cow from a catapult, you could break its velocity down into its speed in the vertical direction (how fast its height is changing) and its speed in the horizontal direction. And each of these components would be measured in “speed units” (miles per hour, or meters per second, or whatever).
They Might Be Giants answered this very question on their recent “science for kids” album “Here Comes Science” (not to imply you’re a kid for not knowing the difference, of course).
Personally, as a chemist I like “Meet the Elements”, especially if if can displace The Element Song by Tom Lehrer - the video is also pretty cool. http://www.youtube.com/watch?v=d0zION8xjbM
To expand a bit on an earlier post, when you are in a car that is going around a curve at constant speed, you nonetheless feel the acceleration by being forced outwards.
I cringe whenever I hear “the velocity of light”. Abstractly, light does not have a velocity. A particular photon will but that’s a different story. Light has a speed.
Escape speed is actually the speed necessary to escape the gravitational pull, plus whatever additional energy is needed to overcome drag. If launched in a direction corresponding to apparent “up”, the only drag will be from molecules of the atmosphere, and the amount of additional energy needed will be relatively small (relative, that is, to the total energy needed).
If instead you were to launch “down”, then the amount of drag would be considerable, and the energy needed to overcome it would be correspondingly large. But the actual speed you would need to attain to escape the gravitational pull of the earth would be the same.
All this is further complicated by the reality that we are unable to impart an instantaneous speed to an object (like a spacecraft) but instead use a motor or series of motors that provide “push” for some interval of time, thus imparting an acceleration and an elevation.
And our hypothetical launch vehicle could “escape” at almost any speed, even quite a low one, as long as we were able to continue to impart sufficient ongoing “push” to overcome gravity. We could “escape” at two miles per hour, as long as we had some magic motor that kept pushing us at that speed for however long it would take to get so far from earth that the planet’s gravity could be considered negligible.
Escape speed is calculated without accounting for drag. Otherwise one couldn’t refer to, for instance, “the escape speed of the Earth”, since drag depends on all sorts of complicated things like the shape of the projectile and the weather conditions at the launch site. The presence of drag does mean that, in practice, a launch speed greater than escape speed would be necessary.
So, we need to accelerate to a speed and a vector that increasingly gets us farther from ignorance, politicians, apathy, laziness, misdirection and deliberate deception and against all objections and resistance so we can become free to the true beauty of everything? Math is the easiest way to express the essence of getting to where we need to be?
I do not think we have developed an driving force strong enough to do that yet, nor do we have the correct vector really nailed down due to the density of some of the obstructions.
“Mr. Scott, we must have more speed. Are the engines powerful enough?”
You’re right-- my first paragraph should have begun with the word “Practical”.
The difference is this:
s
v
One important difference that hasn’t been mentioned is that a vector like velocity can be negative. If we both run at each other at 10 mph, one could say that I have a velocity of 10 mph while you have one of -10mph, though we both have the same speed.
Huh?
That didn’t show up too well, did it.
The “s” was plain text, and the “v” was bolded. Some smart ass will no doubt show up shortly with a font for the little arrow on top.
‘s’ is usually displacment though! Speed would be something along the lines of |v| or perhaps sqrt(v^2). Not that it really matters!!! (as long as your clear and consistent with your definitions of course)
It makes sense to present velcoities as their magnitudes and a single real number (as the reals form a 1-D vector space over themselves wrt real addition and multiplication), but it’s not sufficent when there’s 3 dimensions as you need 3 real numbers to describe a 3 dimensional real vector continiously.
Neither vector is negative. Rather, it’s the ratio between the two vectors which is negative (specifically, it’s the signed scalar -1). Of course, all “negative” means is “has the effect on direction of reversing it”.
Saying “vectors can be negative and scalars cannot” is highly misleading, and in fact opposite from how these terms are usually used.
To throw in my own two cents’ worth:
Velocity is a vector quantity that is composed of a magnitude (e.g. 30 mph) and a direction (e.g. north).
Speed is a scalar quantity composed of only a magnitude.
For a given object, the magnitude of the object’s instantaneous velocity is equivalent to its instantaneous speed.
(I added “instantaneous” because if you are discussing *average *speed and velocity, it gets more complicated. If I make a trip in which my starting point is the same as my ending point, my average velocity is zero, but my average speed is non-zero.)