AP Physics C Equations Flashcards

Kinematics

• Final velocity equation: ( v = v_0 + at )
• Final position equation: ( x = x_0 + v_0 t + \frac{1}{2} at^2 )
• Final velocity squared: ( v^2 = v_0^2 + 2a(x - x_0) )

Forces and Motion

• Net force: ( \sum F = F_{\text{net}} = ma )
• Impulse as integral of force over time: ( J = \int F dt = \Delta p )
• Momentum: ( p = mv )
• Frictional force: ( F_{\text{fric}} \leq \mu N )

Work and Energy

• Work as integral of force along a path: ( W = \int F \cdot dr )
• Kinetic energy: ( K = \frac{1}{2} mv^2 )
• Power related to work: ( P = \frac{dW}{dt} )
• Power as dot product of force and velocity: ( P = F \cdot v )
• Gravitational potential energy: ( \Delta U_g = mgh )

Rotational Motion

• Centripetal acceleration: ( a_c = \frac{v^2}{r} = \omega^2 r )
• Torque: ( \tau = r \times F )
• Net torque: ( \Sigma \tau = \tau_{\text{net}} = I \alpha )
• Rotational inertia: ( I = \int r^2 dm = \Sigma mr^2 )
• Center of mass: ( r_{\text{cm}} = \frac{\sum mr}{\sum m} )

Angular Motion

• Translational velocity in terms of angular velocity: ( v = r \omega )
• Angular momentum: ( L = r \times p = I \omega )
• Rotational kinetic energy: ( K = \frac{1}{2} I \omega^2 )
• Rotational kinematics for final velocity: ( \omega = \omega_0 + \alpha t )
• Rotational kinematics for final position: ( \theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2 )

Oscillations and Law of Springs

• Hooke's law for springs: ( F_s = -kx )
• Elastic potential energy in springs: ( U_s = \frac{1}{2} kx^2 )
• General period of oscillation: ( T = \frac{2\pi}{\omega} = \frac{1}{f} )
• Period of a spring: ( T_s = 2\pi \sqrt{\frac{m}{k}} )
• Period of a pendulum: ( T_p = 2\pi \sqrt{\frac{l}{g}} )

Gravitation

• Gravitational force: ( F_g = -\frac{G m_1 m_2}{r^2} \hat{r} )
• General gravitational potential energy: ( U_g = -\frac{G m_1 m_2}{r} )

Electrostatics

• Coulomb's law: ( F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2} )
• Electric field: ( E = \frac{F}{q} )
• Charge-line integral: ( \oint E \cdot dA = \frac{Q}{\epsilon_0} )
• Differential for electric field: ( E = -\frac{dV}{dr} )
• Electric potential: ( V = \frac{1}{4 \pi \epsilon_0} \sum_i \frac{q_i}{r_i} )
• Electric potential energy: ( U_E = qV = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r} )

Capacitance

• Capacitance relationship: ( C = \frac{Q}{V} )
• Capacitance with dielectric: ( C = \kappa \epsilon_0 \frac{A}{d} )
• Parallel capacitance: ( C_p = \sum_i C_i )
• Capacitance in series: ( \frac{1}{C_s} = \sum_i \frac{1}{C_i} )
• Energy stored in a capacitor: ( U_c = \frac{1}{2} QV = \frac{1}{2} CV^2 )

Current and Resistance

• Current differential: ( I = \frac{dQ}{dt} )
• Resistance formula: ( R = \rho \frac{l}{A} )
• Electric field related to resistivity: ( E = \rho J )
• Current: ( I = Ne v A )

Circuit Laws

• Electric potential simplified: ( V = IR )
• Resistance in series: ( R_s = \sum_i R_i )
• Resistance in parallel: ( \frac{1}{R_p} = \sum_i \frac{1}{R_i} )
• Power in electric circuits: ( P = IV )

Magnetism

• Magnetic force equation: ( F_m = q v \times B )
• Ampere's law: ( \oint B \cdot dl = \mu_0 I )
• Biot-Savart law for magnetic field: ( dB = \frac{\mu_0}{4\pi} \frac{Idl \times r}{r^3} )
• Force on current in a magnetic field: ( F = \int I dl \times B )
• Magnetic field for a series of wires: ( B_s = \mu_0 n I )

Enhance your understanding of key equations in AP Physics C with these flashcards. Each card features important kinematics and dynamics equations essential for mastering the course. Ideal for quick revisions and improving recall before exams.