Deliverables

Create a file named

hw$02.$py that contains the following functions.

Your functions must be named exactly as written below

Include an informative standard$-$conforming docstring for each function

All vectors and matrices must be numpy arrays $($ndarray$)$

dot$\_$product

Returns a scalar that is the dot product of two equal size input vectors

You may assume that the vectors are of equal size; no error checking is required

You must use a loop to compute the dot product

cross$\_$product

Returns a vector that is the cross product of two equal size input vectors

You may assume that the vectors are of equal size; no error checking is required

It must return a $3-$element $1D$ array per the definition of the cross product

matrix$\_$vector$\_$product

Returns a vector that is the product of a matrix and a vector

You may assume that the matrix and vector are compatible for multiplication; no error checking is required

You must use loop$($s$)$ to compute the matrix$-$vector product

plate$\_$velocity

Returns a vector that is the velocity of the plate at the center of plate B$,$ given by Equation $(1)$ with the following input parameters:

$r_B-$ position vector from point $O$ to the center of plate $B$

$-$ angular velocity of the plate about the $z-$axis

The following function signature must be used:

$vb=$ plate$\_$velocity$($rb$,$ w$)$:

You must use the functions described above to compute the plate velocity as appropriate

angular$\_$momentum