# A mechanics problem with moving and fixed coordinate systems

1. Jan 16, 2014

### mech-eng

1. A point P is described in terms of a fixed coordinate system XYZ with unit vectors I,J,K and a moving coordinate system xyx with unit vectors i,j,k.at a given instant the location of the origin
of the moving system is 80I-90J.the velocity of P relative to moving system is 50i+45j;the radius of point P is 3i+4j in the moving system, which rotates at angular velocity w=100k. Find the velocity of point P in the fixed system if the x axis is rotated 30 counterclockwise from the X axis.

2. Relevant equations
R=R0+r
R=R0xI+R0yJ+R0zk+rxi+ryj+rzk
R^=R^0xI+R^0yJ+R^0zK+r^xi+r^yj+r^zk+rxi^+ryj^+rzk^, here ^ represents derivative,i.e it is dot.
3. The attempt at a solution
v=wxr , x:cross product symbol v=300j-400i I dont know where I should use this v and its relation with another V which is 50i +45 j as given in the problem.In this problem I dont clearly understand whether w is belongs to radius or moving coordinates.

Last edited: Jan 16, 2014