Question

how will we know what comes first in cross product?

Answer 1

@Mashy

Answer 2

@Mashy @Mashy

Answer 3

huh?!? what do u mean?!?

Answer 4

L=p x r in vector form

Answer 5

its defined that way. .. :P think about the rotation. its very hard for me to explain like this..

Answer 6

means?

Answer 7

hey ?

Answer 8

if you're talking about the angular momentum of a body moving with momentum p, then l = r x p defines the angular momentum of the body about an axis through the origin - it's a definition

Answer 9

how can u say that r comes first
means explain

Answer 10

i don't see that there is anything to explain, l = r x p defines l, the order of r and p is an arbitrary choice that everyone agrees to use

Answer 11

let it se
thanks 4 ur help @ProfBrainstorm

Answer 12

you're welcome

Answer 13

Keep in mind that the verse of angular momentum is PURELY conventional!! scientists could have chosen the other sense and everything would work the same. Just remember that the cross product (because of this convention) is not commutative that's why r comes always first

Answer 14

thanks @Armi

Answer 15

i did not understand

Answer 16

@Armi
No its not PURELY conventional ..

cross product.. talks about rotation

angular momentum = "how much rotational motion an object would have if it rotated about a pivot"
its r cross p , because, the rotation would take place in that particular sense, and not the other way around

Answer 17

the vector cross product is a mathematical construct that doesn't necessarily represent angular momentum, and it happens to be defined using what we call a right handed convention for the sense of the vector
if we then agree to use the right hand convention for vectors that represent angular momentum, it follows that l = r cross p

Answer 18

even if u do not consider the right hand rule

say you considered the LEFT hand rule as a convention for cross product..
are you saying l would be p cross r in that case @ProfBrainstorm ?

Answer 19

yes, but only if you retained the right hand convention for angular momentum

Answer 20

my question is.. what if u consider the left hand convention?
would you say \[l = p \times r\]
in that case?

Answer 21

i understand your question
if you use the left hand rule to define cross product as a mathematical entity, but retain the right hand convention for defining the angular momentum vector, then you would have to have l=p cross r
if however you adopted the left hand convention universally, then you would have l= r cross p again (i think)

Answer 22

you see, the way we define cross product is independent of the way we define angular momentum, though of course it makes sense for everyone to adopt one convention or the other

Answer 23

"if you use the left hand rule to define cross product as a mathematical entity, but retain the right hand convention for defining the angular momentum vector"

this makes no sense to me..

left hand or the right hand rule is used JUST TO GIVE A DIRECTION for the rotation.. the rotation ITSELF doesn't change.. instead of using left hand or right hand, lets use clockwise or anticlockwise..
don't u agree in that case, there is only one answer. ?

so u cannot define l = p x r ..
l should always be r x p . cause the two rotations are different .. i think of cross products as ROTATIONS.. clockwise or anticlockwise first.. then think about using the thumb rule (which depends on whether left hand or right hand) ..

u have to agree, that the rotation will remain the same.. (physically its the rotation that matters), but depending on the thumb rule.. the DIRECTION (inwards or outwards) might change !

Answer 24

of course the physical rotation must remain the same, it doesn't care about our conventions, i agree completely
however, consider a mass executing circular motion about a point
the position vector and velocity vector define a plane in space
that plane defines a unique direction perpendicular to it
but we can look out of that plane from either side, and whichever side we decide to make the angular momentum vector point out of is just our choice by convention

Answer 25

Lets consider an example.. to tell u what m saying :P.

lets say i wanna calculate the angular momentum of that particle (with momentum P) about the point O.

First.. what is the meaning of angular momentum.
IF that object were to ROTATE about that point O, how much ROTATIONAL momentum it would have ? ..
do u agree in this case the angular momentum MUST BE clockwise??

Answer 26

now lets define this angular momentum .. so we will draw a position vector