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I Direction of 'r' vector

  1. Jul 21, 2016 #1
    So I understand the with torque, T= r x F: r is a vector that points from axis to point of force, correct?

    I am confused about the direction of r is a couple of other circumstances, and I wanted to know if there is handy rule.

    For example a linear momentum, this diagram, does 'r' also point from center of orbit to the mass?

    Also, in Biot-Savart law:

    $$d{\bf{B}} = \frac{{\mu _0 }}{{4\pi }}\frac{{Id\ell \times {\bf{\hat r}}}}{{r^2 }}$$

    what is the direction of 'r' ... from current to the point or the other way around??

    Is there a handy rule?

    Thanks a lot!
     
  2. jcsd
  3. Jul 21, 2016 #2

    A.T.

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    For all possible meanings of "r"? No, but usually it's a vector describing a position, relative to some reference point.
     
  4. Jul 21, 2016 #3

    andrewkirk

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    You are correct in all three cases. For angular momentum the r is from axis to CoM of the object whose angular momentum is being measured. For Biot-savart it is the vector from the wire to the point of measurement.

    The handy rule is that a formula used to define a physical quantity in terms of a cross product will be written in an order that makes the vector of the physical quantity point the way we want it to point. Note how the r is the first argument to the cross product for torque and ang mom and the second argument for Biot-Savart. That's because that's where it needs to be to make the formula work.
     
  5. Aug 6, 2016 #4

    David Lewis

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    You've got the sense of r correct but I wouldn't use the term point of force . You could say instead the head of displacement vector r is a point on the force vector's line of application.
     
  6. Aug 11, 2016 #5

    David Lewis

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    Correction: Should be line of action, not line of application.
     
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