# Math Help - vectors

1. ## 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

2. 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

3. 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 $r^2 = \left ( \sqrt{2^2 + (-1)^2 + 3^2} \right ) ^2 =
14$
.

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