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Math Help - vectors

  1. #1
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    vectors

    1) The centrifugal force acting on an object of mass m kg , with position vector r from the origin, and rotating at a constant angular velocity w radians per second is given by -mw(wXr) Newtons. calculate the centrifugal force vector and its magnitude for an object with m = 3kg,r=-2i+5j+7k metres and w=j+2 radians per sec



    2) An electric charge of q1 coulomb, at a position vector r and moving velocity v1 produces a magnetic induction B given B =
    m vXr
    __ q [_____]
    4pi lrlsquare

    where m is the constant of permeability . The magnetic force F exerted on a second charge of q2 coulombs and moving with velocity v2 is given f=q2v2XB Find the magnetic force F if v1=i+j-k,v2=-3i+j,r=2i-j+3k and q1=q2=1
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cheesepie
    1) The centrifugal force acting on an object of mass m kg , with position vector r from the origin, and rotating at a constant angular velocity w radians per second is given by -mw(wXr) Newtons. calculate the centrifugal force vector and its magnitude for an object with m = 3kg,r=-2i+5j+7k metres and w=j+2 radians per sec
    First off, are you trying to talk about a "centripetal" force?

    Second, when you give the formula F = -mw(wXr) what are you trying to say? I'm guessing: \vec F = -m | \vec w | ( \vec w \times \vec r).

    Finally you said w = \hat j + 2. What direction is the "2" in?

    -Dan
    Last edited by topsquark; July 31st 2006 at 09:56 AM. Reason: Made a boo-boo!
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cheesepie
    2) An electric charge of q1 coulomb, at a position vector r and moving velocity v1 produces a magnetic induction B given B =
    m vXr
    __ q [_____]
    4pi lrlsquare

    where m is the constant of permeability . The magnetic force F exerted on a second charge of q2 coulombs and moving with velocity v2 is given f=q2v2XB Find the magnetic force F if v1=i+j-k,v2=-3i+j,r=2i-j+3k and q1=q2=1
    Ummm... \vec B = \frac{m}{4 \pi} \frac{q_1 \vec v_1 \times \vec r}{r^2}, yes? Then \vec F = q_2 \vec v_2 \times \vec B.

    So. I'll do the vector part. (Ignoring the fact that you haven't given units...)
    \vec v_1 = \hat i + \hat j - \hat k
    \vec v_2 = -3 \hat i + \hat j
    \vec r = 2 \hat i - \hat j + 3 \hat k

    \vec v_1 \times \vec r = \begin{vmatrix} \hat i & \hat j & \hat k \\ 1 & 1 & -1 \\ 2 & -1 & 3 \end{vmatrix}  = 2 \hat i - 5 \hat j - 3 \hat k

    And, of course r^2 = \left ( \sqrt{2^2 + (-1)^2 + 3^2} \right ) ^2 =<br />
14.

    Thus
    \vec v_2 \times \vec B is proportional to
    \begin{vmatrix} \hat i & \hat j & \hat k \\ -3 & 1 & 0 \\ 2 & -5 & -3 \end{vmatrix} = -3 \hat i - 9 \hat j + 13 \hat k.

    -Dan
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