Velocity is the rate of change in distance over change in
time, this can be written as:
v = Δd / Δt
While acceleration is the rate of change in velocity over
change in time, this is written as:
a = Δv / Δt
<span>Both quantities are vector quantities because negative
values means that the acceleration or velocity is acting on the opposite
direction.</span>
I think you forgot to give the options along with the question. I am answering the question based on my knowledge and research. "Radiant to thermal" is the type of energy conversion that occurs when <span>you place your feet near the fireplace and they become warm. I hope the answer has come to your great help.</span>
I think the key here is to be exquisitely careful at all times, and
any time we make any move, keep our units with it.
We're given two angular speeds, and we need to solve for a time.
Outer (slower) planet:
Angular speed = ω rad/sec
Time per unit angle = (1/ω) sec/rad
Angle per revolution = 2π rad
Time per revolution = (1/ω sec/rad) · (2π rad) = 2π/ω seconds .
Inner (faster) planet:
Angular speed = 2ω rad/sec
Time per unit angle = (1/2ω) sec/rad
Angle per revolution = 2π rad
Time per revolution = (1/2ω sec/rad) · (2π rad) = 2π/2ω sec = π/ω seconds.
So far so good. We have the outer planet taking 2π/ω seconds for one
complete revolution, and the inner planet doing it in only π/ω seconds ...
half the time for double the angular speed. Perfect !
At this point, I know what I'm thinking, but it's hard to explain.
I'm pretty sure that the planets are in line on the same side whenever the
total elapsed time is something like a common multiple of their periods.
What I mean is:
They're in line, SOMEwhere on the circles, when
(a fraction of one orbit) = (the same fraction of the other orbit)
AND
the total elapsed time is a common multiple of their periods.
Wait ! Ignore all of that. I'm doing a good job of confusing myself, and
probably you too. It may be simpler than that. (I hope so.) Throw away
those last few paragraphs.
The planets are in line again as soon as the faster one has 'lapped'
the slower one ... gone around one more time.
So, however many of the longer period have passed, ONE MORE
of the shorter period have passed. We're just looking for the Least
Common Multiple of the two periods.
K (2π/ω seconds) = (K+1) (π/ω seconds)
2Kπ/ω = Kπ/ω + π/ω
Subtract Kπ/ω : Kπ/ω = π/ω
Multiply by ω/π : K = 1
(Now I have a feeling that I have just finished re-inventing the wheel.)
And there we have it:
In the time it takes the slower planet to revolve once,
the faster planet revolves twice, and catches up with it.
It will be 2π/ω seconds before the planets line up again.
When they do, they are again in the same position as shown
in the drawing.
To describe it another way . . .
When Kanye has completed its first revolution ...
Bieber has made it halfway around.
Bieber is crawling the rest of the way to the starting point while ...
Kanye is doing another complete revolution.
Kanye laps Bieber just as they both reach the starting point ...
Bieber for the first time, Kanye for the second time.
You're welcome. The generous bounty of 5 points is very gracious,
and is appreciated. The warm cloudy water and green breadcrust
are also delicious.
Answer:
People firstly believe that the planets move in a circular orbit until Newton came up with his hypothesis by inventing calculus so that we could understood and calculated planetary orbits and their accuracy.
Explanation:
- Everyone assumed the planets were perfect circles until Newton came up with an idea. Slowly people would make maps of the orbits that added circles on circles, and they could never really explain about the movement of the planet. They simply say that planets move on circles but they lacked the math to explain or prove it. Then Newton came up with an idea of inventing calculus so that we could understood and calculated planetary orbits and their accuracy.
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- Firstly people used their observations and say that the orbits looked like circles, then they developed their models and did the math, and proposed their hypothesizes which were wrong, until Newton came along and tried to match a model that used elliptical orbits and invented the math that allowed him to make predictions with it. His model worked for most planets.
-
- However he could not explain about the planet Mercury for instance since it was a very strange orbit. Then after the Einstein's theory of General Relativity he could also explain very deeply about it.
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- Scientists and Astronomers made hypothesizes that there was another planet orbiting too close to the sun to see with telescopes, called Vulcan, that explained mercury's orbit before Einstein's theory. Then long after we had telescopes which was good enough to see if there was a planet orbiting closer to the sun than mercury.
The picture is kinda blurry but it looks like granite which is metamorphic.
