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Thread: Product of a vector and its derivative

  1. #1
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    Product of a vector and its derivative

    r.v = rv

    That's what this book says, but I don't buy it.

    If v were tangential to r, the dot product would be zero. But product of their magnitudes could still easily be non-zero.

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    Quote Originally Posted by Glom View Post
    r.v = rv

    That's what this book says, but I don't buy it.

    If v were tangential to r, the dot product would be zero. But product of their magnitudes could still easily be non-zero.
    Which derivative are they using?

  3. #3
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    The dot product as you write it up there is defined as:

    vr = v r cos(θ)

    where the bold are vectors and the non-bold v and r are the magnitude of the vectors and θ is the angle between v and r.

    Now we know that there is a relationship between v and r namely that v = dr/dt, velocity is the temporal derivative of the location vector. So now we get:

    vr = dr/dt•r, but still that will not delete the cos(θ), only when the body is moving in a rectilinear direction.
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