physics 1 refernce

notes/phys1/phys1_ap-reference.txt

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+== 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