ds refers to change in arc length. T is the unit tangent vector, it’s the direction(unit vector) of the velocity vector. It’s basically, how the direction is changing. The change in direction can also be modeled by a change in position with respect to the arc length thus why dr/ds = T
v=dr/dt means velocity is equal to displacement over change in time |v|=ds/dt means speed is equal to distance over change in time ➡️ T=dr/ds=(dr/dt)/(ds/dt)=v/|v| means unit tangent vector is equal to displacement over distance which is also equal to velocity over speed
@@TYLERRAKE-that is called chain rule. It is often used in differentiation of a function which is not respect to x, for example, y=x^2➡️ dy/dx=d(x^2)/dx=2x y=z^2➡️dy/dx=d(z^2)/dx=(d(z^2)/dz)(dz/dx)=2z(dz/dx)
Just as v⃗ is the velocity, its magnitude ds/dt is the speed, often written v (no arrow, no boldface). Then just as dv⃗/dt is the acceleration a⃗, the derivative dv/dt (which appears here as d²s/dt²) is the scalar acceleration a (also called tangential acceleration or colloquial acceleration). Notice that a is _not_ the magnitude of a⃗; instead, a>0 when the object is speeding up, and a
Now do the derivation for curvature k in terms of maagnitude of cross product velocity x acceleration all divided by magnitude of velocity cubed.. as a nice intro to differential geometry!
I get all of it except for the kilonuts at the very end.
its kappa × Normal unit vector i think
I'm pretty sure N is supposed to be a vector, wheres the arrow???
"im pretty sure N is supp-" 🤓☝️
He forgot the arrow oh no 🤓
@@Waller12 notation matters because understanding matters🤡
What exactly is T vector supposed to represent?
Unit tangent vector
Unit tangent. It’s the unit vector of the velocity vector (directional component of velocity vector).
Whats ds and T?
Rest all i understood
ds refers to change in arc length. T is the unit tangent vector, it’s the direction(unit vector) of the velocity vector.
It’s basically, how the direction is changing. The change in direction can also be modeled by a change in position with respect to the arc length thus why dr/ds = T
I like physics, but what is ALL OF THIS?
what is N and k and how did he get it from dT/ds
Me in grade 7 :
Is calculus vector?
What is dr/ds and ds/dt here
v=dr/dt means velocity is equal to displacement over change in time
|v|=ds/dt means speed is equal to distance over change in time
➡️
T=dr/ds=(dr/dt)/(ds/dt)=v/|v|
means unit tangent vector is equal to displacement over distance which is also equal to velocity over speed
So unit tangent vector is unit vector in the direction of velocity vector
@@khoozu7802 why dr/dt =
dr/ds.ds/dt
@@TYLERRAKE-that is called chain rule. It is often used in differentiation of a function which is not respect to x, for example,
y=x^2➡️ dy/dx=d(x^2)/dx=2x
y=z^2➡️dy/dx=d(z^2)/dx=(d(z^2)/dz)(dz/dx)=2z(dz/dx)
@@khoozu7802 I know chain rule but I am not able to see it here
That's what she said
This isn't even math anymore, it's just letters 💀
Basic physics vector analysis of acceleration and velocity vectors Σιγμα
A brick.
What T?
Unit tangent vector
11th grade physics,
In India
9th grade physics here. Get your game up bro
it's 9th grade physics bro.
@@OPGAMER.It's 7th grade physics here in India
@@sohidulislam6020 Where my cousin is he says they took it in 5th grade. That’s why I let him teach me LOL
Isn't this a math problem, not a physics one? Why do you cover this?
I understand nothing!
It's just 9th grade physics here in India
@@sohidulislam6020 5th grade physics where my cousin studies. 9th is too old don’t you think?
@@sereer5887 In India here, Our Education system is not that advanced . I know It's a 5th grade physics but here it's 9th grade physics for us
@@sohidulislam6020Which school u go to?
I'm also from India but it's taught in 11th grade as per cbse
@@epikherolol8189 Online School
Just as v⃗ is the velocity, its magnitude ds/dt is the speed, often written v (no arrow, no boldface). Then just as dv⃗/dt is the acceleration a⃗, the derivative dv/dt (which appears here as d²s/dt²) is the scalar acceleration a (also called tangential acceleration or colloquial acceleration). Notice that a is _not_ the magnitude of a⃗; instead, a>0 when the object is speeding up, and a
ω = 2π/Τ = (2π/λ)×(λ/Τ) = κ ν
@@soyanshumohapatra : Yes, where λ is the circumference of the osculating circle.
@@tobybartels8426 idk bro
I just studied wave motion and only know the formulas
what tf am i looking at
I should write κ⃗ = κN⃗, not κ⃗ = κB⃗, so a⃗ = aT⃗ + v²κ⃗ (in any number of dimensions).
Kinematics with gradients of vectors
Calculus 3 and differential geometry
Always good to see a little calc 3 peeking thru the cracks
sin3x=sin2x+1
Now do the derivation for curvature k in terms of maagnitude of cross product velocity x acceleration all divided by magnitude of velocity cubed.. as a nice intro to differential geometry!
uhhhhhh
V^2=aR。R是曲率半徑。K=1/R。
The other alternative is a=w^2×r