Dynamics Rotating Rod Problem

My teacher would like for us to use the format I am using, however I cannot seem to get some of my equations and/or vectors correct. I am getting an output but it is not right. Does anyone know what I am missing or doing wrong?

clc, clear

% known values
m = 50.0 ;              % mass of the rod in kg
g = 9.81 ;              % acceleration due to gravity, m/s^2
L = 5.0 ;               % length of the rod in meters
W = m*g ;               % weight of the rod in Newtons
theta = 90*pi/180 ;     % angle between the rod and the x-axis

Ia = (1/3)*m*L^2 ;              % moment of inertia equation for point A

mu_s = [0.1, 0.2, 0.3] ;        % coef of static friction
mu_k = [0.075, 0.15, 0.225] ;   % coef of kinetic friction

syms a_Gx a_Gy alpha a_A Ay Ax

% vector equations
alpha_ = alpha*[0 0 1] ;                    % angular acceleration vector
rga_ = (L/2)*[cos(theta) sin(theta) 0] ;  % position vector from A to rod center
A_ = [Ax Ay 0];                             % reaction force at point A
W_ = -W*[0 1 0] ;                           % weight vector
a_G_ = [a_Gx a_Gy 0] ;                      % acceleration vector for point G
a_A_ = a_A*[1 0 0] ;                        % acceleration vector for point A

% system of equations
F_eq = A_ + W_ - m*a_G_ ;                    % sum of forces equation
M_eq = Ia*alpha_ - cross(-rga_,A_) ;         % sum of moments alpha positive CCW
a_eq = cross(alpha_,rga_) - a_G_ ;           % acceleration equation

sol = solve(F_eq(1), F_eq(2), M_eq, a_eq, Ay, Ax, a_Gx, a_Gy, a_A, alpha) ;

alpha = eval(sol.alpha)
a_Gx =  eval(sol.a_Gx)
a_Gy =  eval(sol.a_Gy)
a_A =   eval(sol.a_A)
Ay =    eval(sol.Ay)
Ax =    eval(sol.Ax)