Kinematics
Approached this and got the distance at given time from center to be $\frac{a*e^{-2 \sqrt{3} \pi}}{\sqrt{3}}$. But how to approach the distance travelled in the same duration?
32 Replies
SirLancelotDuLac
@Gyro Gearloose
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what in the world
i dont get what it means by revolution
how is it even completing a revolution , theyll meet at O
btw , source?
HCV ka example hai jisme ye Motion explain kiya hai
but i never thought ispe numerical bhi banega
I think it goes in circular path for one revolution
Or maybe a triangular path
Because the v is directing that way
Basically what I have tried till now
ignoring that mosiac thingy nothing is revolving around o
thats what am saying
its a spiraly like path
to o
Each particle has a component of velocity perpendicular to radial vector which gives an angular velocity whoch causes rotation imo
i meant to say
it does not complete any revolution
It is combined rotational motion with radial motion combined ig
💀
Close to O the value of tangential velocity is usin(30) so omega is usin(30)/r
This grows arbitrarily large as object nears O
So, it completes large number of revolutions for all values of v ig.
doesnt revolution basically mean orbitting
Idk. Maybe they meant that the orientation of the triangle rotates by 360 degree
@SirLancelotDuLac https://www.surendranath.org/GPA/Kinematics/Chase/Chase.html?utm_source=chatgpt.com
it dosnt rotate by 360 degrees
Interesting. Is this completely till the end?
yes
Because this means that omega can grow arbitrarily large for r tending to zero
i saw with more particles and noticed that more particles = more revolutions
but with 3 particles it does not revolve
yes it will but it will stop
and it wont revolve in any physical sense
Ah you're right. r/radial component of velocity tends to zero too so we get zeroinfinity kinda thing above
No wait, we get r=a/sqrt(3)e^{-sqrt(3)theta} so for r to tend to zero, theta must tend to infinity?
Either the math is not mathing or the physics is not physicing, I don't know which :sweaty:
oh man but thats not even physically possible i think
they will meet at centroid
and before meeting yes it will tend to infinity
but after meeting
it will just stop
Ah yes, it could be like that sort of pattern where when you zoom in it just seems to rotate or something.
Zooming this in makes this seem apparent ig.
woh toh bohot basic hai as compared to this
u still cant term it at "one revolution" tho
this is "distance covered by particle" ??
Yeah.
got smthin for this?
Ah yes, I think I figured it out
Length of path will be integral of sqrt(r^2+(dr/dtheta)^2) d(theta) and not only r d(theta)
That gives B.
+solved @Gamertug @hardcoreisdead
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