== CONSTANTS ==
G=6.67E-11 m^3/(kg-s^2) (gravitational)
g=9.8 m/s^2 (Earth gravity)
g=9.8 N/kg (gravitational field)
1 atm = 1.0E5 N/m^2 = 1.0E5 Pa

== KINEMATICS ==
v_x = v_x0 + a_x*t
x = x_0 + v_x0*t + 0.5*a_x*t^2
v_x^2 = v_x0^2 + 2*a_x*(x-x_0)

== DYNAMICS ==
x_cm = sum(m_i*x_i) / sum(m_i)
a_sys = sum(F) / m_sys = F_net / m_sys
F_g = G*m_1*m_2/r^2
F_f <= mu*F_N
F_s = -k*delta_x
a_c = v^2/r

== ENERGY ==
K = 0.5*m*v^2
W = F_parallel*d = F*d*cos(theta)
delta_K = sum(W_i) = sum(F_parallel_i*d_i)
U_s = 0.5*k*(delta_x)^2
U_G = -G*m_1*m_2/r
delta_U_g = m*g*delta_y
P_avg = W/delta_t = delta_E/delta_t
P_inst = F_parallel*v = F*v*cos(theta)

== MOMENTUM ==
p = m*v
F_net = delta_p/delta_t = m*delta_v/delta_t = m*a
J = F_avg*delta_t = delta_p
v_cm = sum(p_i) / sum(m_i) = sum(m_i*v_i) / sum(m_i)

== ROTATION ==
omega = omega_0 + alpha*t
theta = theta_0 + omega_0*t + 0.5*alpha*t^2
omega^2 = omega_0^2 + 2*alpha*(theta-theta_0)
v = r*omega
a_T = r*alpha
tau = r_perp*F = r*F*sin(theta)
I = sum(m_i*r_i^2)
I' = I_cm + M*d^2
alpha_sys = sum(tau) / I_sys = tau_net / I_sys
K = 0.5*I*omega^2
W = tau*delta_theta
L = I*omega
L = m*v*r*sin(theta)
delta_L = tau*delta_t
delta_x_cm = r*delta_theta
T = 1/f
T_s = 2*pi*sqrt(m/k) (spring)
T_p = 2*pi*sqrt(l/g) (pendulum)
x = A*cos(2*pi*f*t) or x = A*sin(2*pi*f*t)

== FLUIDS ==
rho = m/V
P = F_perp/A
P = P_0 + rho*g*h
P_gauge = rho*g*h
F_b = rho*V*g
A_1*v_1 = A_2*v_2
P_1 + rho*g*y_1 + 0.5*rho*v_1^2 = P_2 + rho*g*y_2 + 0.5*rho*v_2^2

== GEOMETRY ==
Rectangle: A = b*h
Triangle: A = 0.5*b*h
Circle: A = pi*r^2, C = 2*pi*r, s = r*theta
Solid: V = l*w*h
Cylinder: V = pi*r^2*l, S = 2*pi*r*l + 2*pi*r^2
Sphere: V = 4/3*pi*r^3, S = 4*pi*r^2
Right triangle: a^2+b^2=c^2
sin(theta) = a/c, cos(theta) = b/c, tan(theta) = a/b

== COMMON ANGLES ==
theta=0: sin=0, cos=1, tan=0
theta=30: sin=0.5, cos=sqrt(3)/2, tan=sqrt(3)/3
theta=37: sin=3/5, cos=4/5, tan=3/4
theta=45: sin=sqrt(2)/2, cos=sqrt(2)/2, tan=1
theta=53: sin=4/5, cos=3/5, tan=4/3
theta=60: sin=sqrt(3)/2, cos=0.5, tan=sqrt(3)
theta=90: sin=1, cos=0, tan=infinity