Rotating Axes
Description
Demonstration of vector components projected to a new axis pair. The new axes are rotated by an angle .
The steps for computing the components on the new axes using the step button (Double right triangles)
1. The original x and y vector components
2. Show new axes pair and angle alpha
3. Project the y component to the new x axis,
4. Project the y component to the new y axis,
5. Project the x component to the new x axis,
6. Project the x component to the new y axis,
The final operation is to add the new components on each axis.
Note that these two equation can be written in matrix form
Alternate Angle Method
Another method is to use the magnitude and angles of the vectors.
The magnitude of the original vector,
and the angle of the original vector using the arctangent adding or subtracting 180o if Vx is negative.
Then the angle of the vector with respect to the new coordinates is and the magnitude stays the same. Therefor the new components become and