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Simple qn on vectors and scalars

  1. Feb 20, 2005 #1
    ok...
    Is it possible to use the formula to decide whther a physical quantity is a scalar or a vector?

    eg:
    Velocity=change in displacement/time

    Thus, since displacement is a vector,
    therefore, velocity is also a vector>?

    And for density...
    Density=mass/volume

    SInce mass and volume are both scalar,
    Therefore, density is a scalar>?
     
    Last edited: Feb 20, 2005
  2. jcsd
  3. Feb 20, 2005 #2
    Yes and yes. If the input to a formula is a vectors or vectors then the answer to the formula will be a vector. Unless that is the formula has a dot product, or absolute value. Or in some cases it is possible to take one component of a vector and use that as a scalar answer.
     
  4. Feb 20, 2005 #3

    dextercioby

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    With 2 vectors in 3D multiple operations can be made and the result can be
    1.A scalar.
    2.A pseudovector.
    3.A vector.
    4.A second rank tensor...

    Daniel.
     
  5. Feb 20, 2005 #4

    cepheid

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    Hey Daniel, that's interesting. So, I'm assuming that you arrive at 1 using the dot product, and 3 using the cross product. But what is a pseudovector? How do you make one? And is a second-rank tensor just a matrix? Again, how do you combine the two vectors to make one? Thanks.

    I hope the answer will not be too hard for me to understand...
     
  6. Feb 20, 2005 #5

    dextercioby

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    Not really.At a vector you reach by vector-space operations...Addition and scalar multiplication.Cross-product is a special case of exterior product and the result is a pseudovector...As for second rank tensor,well it's the tensor/dyadic (ancient name) product...Scalar product (inner product) is just a contracted tensor product.

    Daniel.
     
  7. Feb 20, 2005 #6
    But... how about work done, potential energy and kinetic energy?

    eg:
    Work done=force*distance
    work done=mass *acceleration*distance

    Acceleration is a vector but that doesn't mean work done is a vector too rite?
     
    Last edited: Feb 20, 2005
  8. Feb 20, 2005 #7

    dextercioby

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    "distance" is not a scalar...It is the "displacement vector"...In the definition of work,there is a dot/scalar product which makes the result a scalar...

    Daniel.
     
  9. Feb 21, 2005 #8
    Gunblaze, the answer to your question have to do with vector multiplication, which I am guessing you have not been exposed to.

    F = ma (bold quantities are vectors)

    This equation is a scalar times a vector. The reason they are called scalars is that they will scale a in to a different vector F

    Now look at work:

    [tex]W = \vec{F} \cdot \vec{d}[\tex]

    This is a multiplication of two vectors, fundamentally different than Newtons Second law. Notice that the answer is a number (a scalar) , so this is a scalar product between vectors. Another example:

    [tex]KE = \frac{1}{2}m(\vec{v})^2 = \frac{1}{2}m\ vec{v} \cdot \vec{v}[\tex]

    So kinetic energy, again a scalar, is a product of v with itself.
     
  10. Feb 22, 2005 #9
    How do you graphically add vectors? For example Vector A is equal to a force of .980 N at a compass angle of 35 degrees and Vector B has a force of 1.96 N at 165 degrees.
     
  11. Feb 23, 2005 #10

    dextercioby

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    If u've given not only modulus,but also angles,then those angles are defined wrt certain axis of coordinates.Then u'll simply add their components...

    Daniel.
     
  12. Feb 23, 2005 #11
    Well, the strategy for 2D is this. Choose a coordinate system, with one of the axes preferably along one of the vectors. Find the angles that the vecotrs make with the axes, and break into x and y components. Find the moduli of the components by multiplying with [tex]sin[/tex] or [tex]cos[/tex] and give (+) or (-) signs to the components, then add them as scalars to get the net x and y components.
    To get the modulus of the resulting vector use the Pythagorean theorem, while to get the angle use the [tex]arctan[/tex].
     
  13. Feb 24, 2005 #12
    I'm curious as to when you use each method between 2 vectors. I've just been following equations up until now, but i would like to understand why, and for what reason (and to what end) i use the cross product between vectors, and when the dot. In what situations does one use each method??
     
  14. Feb 24, 2005 #13

    dextercioby

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    Depends of what he wishes to write.Usually,quantities are DEFINED using these matematical operations (with vectors),and therefore your last question loses meaning.


    Daniel.
     
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