Grade 12 Physics formula sheet: printable

Physics 12-1 x-Component from Magnitude and Angle

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

Resolves a vector into its horizontal part from the vector's length and the angle it makes with the…

Physics 12-2 y-Component from Magnitude and Angle

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

Resolves a vector into its vertical part from the vector's length and the angle it makes with the…

Physics 12-3 Right-Triangle Sine Ratio (SOH)

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

Relates an acute angle of a right triangle to its opposite side and the hypotenuse.

Physics 12-4 Right-Triangle Cosine Ratio (CAH)

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

Relates an acute angle of a right triangle to its adjacent side and the hypotenuse.

Physics 12-5 Resultant of Two Vectors at an Angle

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

Finds the magnitude of the sum of two vectors from their lengths and the angle between them, the…

Physics 12-6 Magnitude of a 2D Vector

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

Finds the length of a two-dimensional vector from its x- and y-components, the Pythagorean theorem…

Physics 12-7 Direction Angle of a 2D Vector

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

Gives the direction a two-dimensional vector points, measured counterclockwise from the positive…

Physics 12-8 Newton's Second Law

F = m a

Force equals mass times acceleration.

Physics 12-9 Kinetic Friction Force (f = μₖN)

f_k = \mu_k N

Friction force resisting a sliding surface, equal to the coefficient of kinetic friction times the…

Physics 12-10 Weight (W = mg)

W = m g

Weight of a mass at Earth's surface, using standard gravity g = 9.80665 m/s² (exact by definition).

Physics 12-11 Maximum Static Friction (f = μₛN)

f_{s,\max} = \mu_s N

Largest static friction force available before an object breaks loose and slides, from the static…

Physics 12-12 Angle of Repose (μ = tan θ)

\mu_s = \tan\theta

Steepest angle a surface can be tilted before an object slides, where the coefficient of static…

Physics 12-13 Normal Force on an Incline (N = mg cos θ)

N = m g \cos\theta

Normal force pressing a resting mass into an incline, equal to the component of its weight…

Physics 12-14 Weight Component Along an Incline (mg sin θ)

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

Component of an object's weight acting down the slope of an incline: the force that drives it…

Physics 12-15 Acceleration Down a Frictionless Incline

a = g \sin\theta

Acceleration of an object sliding freely down a frictionless incline, set only by gravity and the…

Physics 12-16 Acceleration Down an Incline with Friction

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

Acceleration of an object sliding down an incline once kinetic friction opposes the motion, from…

Physics 12-17 Final Velocity (Uniform Acceleration)

v = v_0 + a t

Final velocity after accelerating uniformly from an initial velocity for a given time.

Physics 12-18 Centripetal Force (F = mv²/r)

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

Net inward force required to keep a mass moving in a circle at constant speed.

Physics 12-19 Centripetal Acceleration (a = v²/r)

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

Inward acceleration of an object moving in a circle at constant speed.

Physics 12-20 Maximum Speed on a Flat Curve

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

Fastest a vehicle can round a flat, unbanked curve before friction can no longer supply the…

Physics 12-21 Banked Curve Angle

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

Bank angle that lets a vehicle round a curve of a given radius at a given speed with no reliance on…

Physics 12-22 Linear Momentum (p = mv)

p = m v

Momentum as the product of an object's mass and velocity.

Physics 12-23 Impulse (J = FΔt)

J = F \, \Delta t

Impulse delivered by an average force acting over a contact time, equal to the change in momentum.

Physics 12-24 Conservation of Momentum (Two Bodies)

m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2

Conservation of linear momentum in a two-body collision, solving any one mass or velocity from the…

Physics 12-25 Perfectly Inelastic Collision

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

Common velocity of two bodies that stick together after a perfectly inelastic collision, from…

Physics 12-26 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}

Final velocity of the first body in a one-dimensional elastic collision, where both momentum and…

Physics 12-27 Coefficient of Restitution

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

Ratio of separation speed to approach speed in a collision, measuring how much of the relative…

Physics 12-28 Bounce Height from Coefficient of Restitution

h_2 = e^{2} h_1

Height a dropped ball rebounds to, from the drop height and the coefficient of restitution of the…

Physics 12-29 Work (W = Fd cos θ)

W = F d \cos\theta

Work done by a constant force acting at an angle to the displacement.

Physics 12-30 Kinetic Energy

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

Energy of a mass in motion.

Physics 12-31 Work–Energy Theorem

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

Net work done on an object equals its change in kinetic energy, linking force and distance to a…

Physics 12-32 Gravitational Potential Energy (U = mgh)

U = m g h

Energy stored by raising a mass to height h near Earth's surface, with g = 9.80665 m/s².

Physics 12-33 Hooke's Law

F = k x

Restoring force of an ideal spring, proportional to its displacement from rest.

Physics 12-34 Elastic Potential Energy

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

Energy stored in an ideal spring displaced x from its rest length.

Physics 12-35 Power (P = W/t)

P = \frac{W}{t}

Average power as work or energy delivered per unit time.

Physics 12-36 Power from Force and Velocity (P = Fv)

P = F v

Instantaneous power delivered by a force parallel to the velocity.

Physics 12-37 Newton's Law of Universal Gravitation

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

Attractive force between two masses, with G = 6.6743 × 10⁻¹¹ m³ kg⁻¹ s⁻² (CODATA 2018).

Physics 12-38 Gravitational Field Strength

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

Gravitational acceleration produced by a mass M at distance r from its centre.

Physics 12-39 Orbital Velocity

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

Speed of a body in a circular orbit of radius r around a central mass M.

Physics 12-40 Orbital Period

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

Time for one circular orbit of radius r around a central mass M: Kepler's third law in Newtonian…

Physics 12-41 Speed in Circular Motion (v = 2πr/T)

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

Speed of an object in uniform circular motion: one circumference (2πr, with π ≈ 3.14159265) per…

Physics 12-42 Kepler's Third Law (Ratio Form)

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

For two bodies orbiting the same central mass, the squares of their periods are in the same ratio…

Physics 12-43 Escape Velocity

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

Minimum launch speed needed to escape the gravity of a mass M starting from distance r, with no…

Physics 12-44 Gravitational Potential Energy (Orbital)

U = -\frac{GMm}{r}

Gravitational potential energy of a mass m at distance r from a central mass M, taking zero at…

Physics 12-45 Coulomb's Law

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

Electrostatic force between two point charges, with kₑ = 8.9875517923×10⁹ N·m²/C².

Physics 12-46 Electric Charge (Q = It)

Q = I t

Total charge transferred by a steady current flowing for a given time.

Physics 12-47 Capacitance (C = Q/V)

C = \frac{Q}{V}

Defines capacitance as the charge stored per volt applied across a capacitor.

Physics 12-48 Energy Stored in a Capacitor

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

Energy banked in a capacitor's electric field from its capacitance and voltage.

Physics 12-49 Magnetic Force on a Moving Charge

F = q v B \sin\theta

Magnitude of the magnetic (Lorentz) force on a charge moving through a magnetic field.

Physics 12-50 Magnetic Force on a Current-Carrying Wire

F = B I L \sin\theta

Magnitude of the force on a straight current-carrying wire in a uniform magnetic field.

Physics 12-51 Force Between Parallel Wires

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

Magnetic force between two parallel current-carrying wires separated by distance d.

Physics 12-52 Magnetic Field of a Solenoid

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

The uniform field inside a long coil of N turns and length L carrying current I.

Physics 12-53 Magnetic Flux (Φ = BA cos θ)

\Phi = B A \cos\theta

The magnetic field threading a surface: field times area times the cosine of the tilt angle.

Physics 12-54 Faraday's Law of Induction

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

The EMF induced in a coil of N turns by flux changing at ΔΦ/Δt (magnitude form).

Physics 12-55 Motional EMF (ε = BLv)

\varepsilon = B L v

Voltage generated across a conductor of length L moving at speed v through a field B.

Physics 12-56 Wave Speed (v = fλ)

v = f \lambda

The universal wave equation: a wave's speed equals its frequency times its wavelength.

Physics 12-57 Period-Frequency Relation

T = \frac{1}{f}

Period and frequency are reciprocals: seconds per cycle versus cycles per second.

Physics 12-58 Index of Refraction (n = c/v)

n = \frac{c}{v}

How much a medium slows light: the ratio of c to the speed of light in the medium.

Physics 12-59 Snell's Law of Refraction

n_1 \sin\theta_1 = n_2 \sin\theta_2

Light bends at an interface so that n sin θ stays the same on both sides.

Physics 12-60 Critical Angle for Total Internal Reflection

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

Beyond this angle of incidence, light in the denser medium reflects totally instead of refracting.

Physics 12-61 Apparent Depth

d' = \frac{d}{n}

Viewed from straight above, an object under water appears at depth d/n.

Physics 12-62 Double-Slit Fringe Spacing

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

Spacing between adjacent bright fringes on a screen a distance L behind two slits d apart.

Physics 12-63 Diffraction Grating Equation

m \lambda = d \sin\theta

Bright beams leave a grating at angles where the path difference d sin θ is a whole number of…

Physics 12-64 Brewster's Angle

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

The incidence angle at which reflected light is completely polarized.

Physics 12-65 Thin-Film Constructive Interference (Bright Reflection)

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

Bright-reflection condition for a thin film with one half-wave inversion: twice the optical…

Physics 12-66 Thin-Film Destructive Interference (Dark Reflection)

2 n t = m \lambda

Dark-reflection condition for a thin film with one half-wave inversion: twice the optical thickness…