Grade 12 Physics formula sheet — printable

x-Component from Magnitude and Angle

v_x = |\vec{v}| \cos\theta

y-Component from Magnitude and Angle

v_y = |\vec{v}| \sin\theta

Right-Triangle Sine Ratio (SOH)

\sin\theta = \frac{o}{h}

Right-Triangle Cosine Ratio (CAH)

\cos\theta = \frac{a}{h}

Resultant of Two Vectors at an Angle

R = \sqrt{A^2 + B^2 + 2AB\cos\theta}

Magnitude of a 2D Vector

|\vec{v}| = \sqrt{v_x^2 + v_y^2}

Direction Angle of a 2D Vector

\theta = \operatorname{atan2}(v_y,\; v_x)

Newton's Second Law

F = m a

Kinetic Friction Force (f = μₖN)

f_k = \mu_k N

Weight (W = mg)

W = m g

Maximum Static Friction (f = μₛN)

f_{s,\max} = \mu_s N

Angle of Repose (μ = tan θ)

\mu_s = \tan\theta

Normal Force on an Incline (N = mg cos θ)

N = m g \cos\theta

Weight Component Along an Incline (mg sin θ)

F_{\parallel} = m g \sin\theta

Acceleration Down a Frictionless Incline

a = g \sin\theta

Acceleration Down an Incline with Friction

a = g\left(\sin\theta - \mu_k \cos\theta\right)

Final Velocity (Uniform Acceleration)

v = v_0 + a t

Centripetal Force (F = mv²/r)

F_c = \frac{m v^2}{r}

Centripetal Acceleration (a = v²/r)

a_c = \frac{v^2}{r}

Maximum Speed on a Flat Curve

v_{\max} = \sqrt{\mu_s g r}

Banked Curve Angle

\theta = \arctan\!\left(\frac{v^{2}}{r g}\right)

Linear Momentum (p = mv)

p = m v

Impulse (J = FΔt)

J = F \, \Delta t

Conservation of Momentum (Two Bodies)

m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2

Perfectly Inelastic Collision

v = \frac{m_1 u_1 + m_2 u_2}{m_1 + m_2}

Elastic Collision — Final Velocity of Body 1

v_1 = \frac{\left(m_1 - m_2\right) u_1 + 2 m_2 u_2}{m_1 + m_2}

Coefficient of Restitution

e = \frac{v_2 - v_1}{u_1 - u_2}

Bounce Height from Coefficient of Restitution

h_2 = e^{2} h_1

Work (W = Fd cos θ)

W = F d \cos\theta

Kinetic Energy

E_k = \tfrac{1}{2} m v^{2}

Work–Energy Theorem

W = \tfrac{1}{2} m \left(v^{2} - v_0^{2}\right)

Gravitational Potential Energy (U = mgh)

U = m g h

Hooke's Law

F = k x

Elastic Potential Energy

U = \tfrac{1}{2} k x^{2}

Power (P = W/t)

P = \frac{W}{t}

Power from Force and Velocity (P = Fv)

P = F v

Newton's Law of Universal Gravitation

F = \frac{G m_1 m_2}{r^2}

Gravitational Field Strength

g = \frac{GM}{r^{2}}

Orbital Velocity

v = \sqrt{\frac{GM}{r}}

Orbital Period

T = 2\pi \sqrt{\frac{r^{3}}{GM}}

Speed in Circular Motion (v = 2πr/T)

v = \frac{2\pi r}{T}

Kepler's Third Law (Ratio Form)

\frac{T_1^{2}}{T_2^{2}} = \frac{a_1^{3}}{a_2^{3}}

Escape Velocity

v = \sqrt{\frac{2GM}{r}}

Gravitational Potential Energy (Orbital)

U = -\frac{GMm}{r}

Coulomb's Law

F = \frac{k_e \, q_{1} q_{2}}{r^{2}}

Electric Charge (Q = It)

Q = I t

Capacitance (C = Q/V)

C = \frac{Q}{V}

Energy Stored in a Capacitor

E = \tfrac{1}{2} C V^{2}

Magnetic Force on a Moving Charge

F = q v B \sin\theta

Magnetic Force on a Current-Carrying Wire

F = B I L \sin\theta

Force Between Parallel Wires

F = \frac{\mu_0 I_1 I_2 \ell}{2\pi d}

Magnetic Field of a Solenoid

B = \frac{\mu_0 N I}{L}

Magnetic Flux (Φ = BA cos θ)

\Phi = B A \cos\theta

Faraday's Law of Induction

\varepsilon = N \frac{\Delta\Phi}{\Delta t}

Motional EMF (ε = BLv)

\varepsilon = B L v

Wave Speed (v = fλ)

v = f \lambda

Period-Frequency Relation

T = \frac{1}{f}

Index of Refraction (n = c/v)

n = \frac{c}{v}

Snell's Law of Refraction

n_1 \sin\theta_1 = n_2 \sin\theta_2

Critical Angle for Total Internal Reflection

\sin\theta_c = \frac{n_2}{n_1}

Apparent Depth

d' = \frac{d}{n}

Double-Slit Fringe Spacing

\Delta y = \frac{\lambda L}{d}

Diffraction Grating Equation

m \lambda = d \sin\theta

Brewster's Angle

\tan\theta_B = \frac{n_2}{n_1}

Thin-Film Constructive Interference (Bright Reflection)

2 n t = \left(m + \tfrac{1}{2}\right)\lambda

Thin-Film Destructive Interference (Dark Reflection)

2 n t = m \lambda