Translation or parallel movts of vectors

  • #1

Main Question or Discussion Point

my teacher says that vectors can be translates which is fine... but hw can they be moved paralaly without couple acting on it//??
 

Answers and Replies

  • #2
tiny-tim
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hi phyeinstein_c! :wink:
my teacher says that vectors can be translates which is fine... but hw can they be moved paralaly without couple acting on it//??
i think you're confusing a bound vector with a free vector (i've forgotten the correct names, but it's something like that :redface:) …

force is a bound vector, and so its line of application has to be included when specifying it

velocity is a free vector, and you can shove it around so as to put it on the end of another vector

so free vectors do translate, but bound vectors like force (as you say) don't :smile:
 
  • #3
but if velocity vector mover parallaly from one end of a rigid body (not point mass) then it generates torque right??
 
  • #4
tiny-tim
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hi phyeinstein_c! :smile:
but if velocity vector mover parallaly from one end of a rigid body (not point mass) then it generates torque right??
hmm, let me think :rolleyes:

yes, a force vector certainly generates torque (and a momentum vector generates angular momentum , and momentum is simply mass times a velocity vector :redface:) …

perhaps i should have said that relative velocity is a free vector, and you can shove it around so as to put it on the end of another vector! :biggrin:
 
  • #5
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but if velocity vector mover parallaly from one end of a rigid body (not point mass) then it generates torque right??
This statement is nonsense.

First, if one part of a rigid body possesses a certain velocity (vector) then all parts posess the same vector. That is a definition of a rigid body.

So velocity vectors cannot move around a rigid body willy nilly.

Second, velcocity cannot produce torque under any circumstances. That is the province of forces or couples.

Tinytim has already said that force is a bound vector, which means you cannot move it about. What he did not say is that bound vectors also have an origin or point of application as part of their specification.

So if you change the point of application of a force, yes you will induce different moments in a rigid body.

Finally for the record couples are free vectors which may be moved about.
 
  • #6
ok sry by torque i meant rotation.... velocity will be uniform is a case... but when the vector has been taken to one end of the body.. it shud rotate...couple will act only for forces right.
 
  • #7
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ok sry by torque i meant rotation.... velocity will be uniform is a case... but when the vector has been taken to one end of the body.. it shud rotate...couple will act only for forces right.
What do you mean?
 
  • #8
i mean when the velocity vector is shifted from the centre to one end..... parallally.... the body has higher velocity on one end and less on the other... so it should rotate...??
 
  • #9
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Let us start again at the beginning.

What system are you describing?

Is your rigid body translating or rotating about a pivot?
 
  • #10
mathwonk
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a mathematician will not understand a word you guys are saying. mathematically a vector in Euclidean space is an equivalence class of parallel arrows all with same direction and magnitude, and all having different endpoints. Any one of those arrows represents the vector. In that sense we say vectors can be translated. Some say more abstractly that a vector IS a translation of space, and is represented by the arrow drawn from any point to its translated image.

In applying the concept you may wish to distinguish between an individual arrow, and the class it represents. maybe this is what you call free and bound vectors, but i have never heard of them.

I chime in here because i thought maybe your teacher is a mathematician and does not know what you are talking about either.
 
  • #11
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In applying the concept you may wish to distinguish between an individual arrow, and the class it represents. maybe this is what you call free and bound vectors, but i have never heard of them.
Yup that's about it (I'm well known for my precise mathematical statements :biggrin:).
 
  • #12
tiny-tim
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hi mathwonk! :smile:
In applying the concept you may wish to distinguish between an individual arrow, and the class it represents. maybe this is what you call free and bound vectors, but i have never heard of them.
i'm sorry to disillusion you, but wikipedia has heard of them, see http://en.wikipedia.org/wiki/Euclidean_vector" [Broken] …

As an arrow in Euclidean space, a vector possesses a definite initial point and terminal point. Such a vector is called a bound vector. When only the magnitude and direction of the vector matter, then the particular initial point is of no importance, and the vector is called a free vector.​

(though it then seems to get lost, see http://en.wikipedia.org/wiki/Euclidean_vector#In_Cartesian_space" :frown:)
 
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  • #13
Let us start again at the beginning.

What system are you describing?

Is your rigid body translating or rotating about a pivot?
its a rigid body translating...
 
  • #14
a mathematician will not understand a word you guys are saying. mathematically a vector in Euclidean space is an equivalence class of parallel arrows all with same direction and magnitude, and all having different endpoints. Any one of those arrows represents the vector. In that sense we say vectors can be translated. Some say more abstractly that a vector IS a translation of space, and is represented by the arrow drawn from any point to its translated image.

In applying the concept you may wish to distinguish between an individual arrow, and the class it represents. maybe this is what you call free and bound vectors, but i have never heard of them.

I chime in here because i thought maybe your teacher is a mathematician and does not know what you are talking about either.
neither did i ever hear of such bounded vectors.... in any VECTOR by definition its only REPRESENTATION of magnitude and direction..... hw does it matter if it is bounded or unbounded or free....
 
  • #15
hi mathwonk! :smile:


i'm sorry to disillusion you, but wikipedia has heard of them, see http://en.wikipedia.org/wiki/Euclidean_vector" [Broken] …

As an arrow in Euclidean space, a vector possesses a definite initial point and terminal point. Such a vector is called a bound vector. When only the magnitude and direction of the vector matter, then the particular initial point is of no importance, and the vector is called a free vector.​

(though it then seems to get lost, see http://en.wikipedia.org/wiki/Euclidean_vector#In_Cartesian_space" :frown:)
can u discuss some cases (examples) of the 2 cases u metioned..
 
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  • #16
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in any VECTOR by definition its only REPRESENTATION of magnitude and direction
No there is more to it than just magnitude and direction.

Suppose I started in London and travelled 300 mile due north, turned and then travelled 300 miles due west.

Now suppose I did it the other way around ie 300 miles west then 300 miles north.

Would I be in the same place the second time around?

It is an important, and not often stated, requirement that

vector(a) + vector(b) = vector(b) + vector(a)

This is another way of saying that a+b is given by the parallelogram law.
 
  • #17
ohkk thats there but how does it matter in physics... the result of both is u have had the same displacement and u will have the same velocity etc. during both kind of journey.
 
  • #18
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ohkk thats there but how does it matter in physics... the result of both is u have had the same displacement and u will have the same velocity etc. during both kind of journey.
Since the English was so mangled I have no idea what you mean.

Was this an answer to my question,

"Would you end up in the same place either way?"

If, so was your answer yes or no?
 

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