Physics Formula Reference

Formula reference for CSCA preparation

Mechanics

Name	Formula	Unit
Velocity	$v = \frac{\Delta x}{\Delta t}$	m/s
Acceleration	$a = \frac{\Delta v}{\Delta t}$	m/s²
Uniform acceleration	$v = v_0 + at$ Applies when: Constant acceleration a; take the initial velocity direction as positive How the real exam asks it	-
Displacement	$x = v_0 t + \frac{1}{2}at^2$ Applies when: Constant acceleration a; pair with v²−v₀²=2ax to eliminate time How the real exam asks it	m
Velocity-displacement	$v^2 = v_0^2 + 2ax$	-
Free fall	$h = \frac{1}{2}gt^2$ Applies when: Released from rest under gravity alone, air resistance neglected How the real exam asks it	m
Newton's 2nd Law	$F = ma$ Applies when: Acceleration is along the net force; valid for macroscopic bodies at low speed in an inertial frame How the real exam asks it	N
Gravity	$W = mg$	N
Friction	$f = \mu N$	N
Universal gravitation	$F = \frac{Gm_1 m_2}{r^2}$	N
Work	$W = Fs\cos\theta$ Applies when: θ is the angle between force and displacement; work is negative when θ>90° How the real exam asks it	J
Kinetic energy	$E_k = \frac{1}{2}mv^2$ Applies when: A scalar, never negative, independent of the direction of motion How the real exam asks it	J
Gravitational PE	$E_p = mgh$ Applies when: h is measured from the chosen zero level; the sign of Eₚ depends on that choice How the real exam asks it	J
Elastic PE	$E_p = \frac{1}{2}kx^2$	J
Power	$P = \frac{W}{t} = Fv$	W
Momentum	$p = mv$ Applies when: A vector, directed along the velocity How the real exam asks it	kg·m/s
Impulse	$I = Ft = \Delta p$	N·s
Centripetal acceleration	$a_n = \frac{v^2}{r} = \omega^2 r$ Applies when: Always directed at the centre; it changes the direction of the velocity, not its magnitude How the real exam asks it	m/s²
Centripetal force	$F_n = \frac{mv^2}{r}$	N

Electricity & Magnetism

Name	Formula	Unit
Coulomb's Law	$F = \frac{kq_1 q_2}{r^2}$ Applies when: Point charges in vacuum; k is the electrostatic constant How the real exam asks it	N
Electric field	$E = \frac{F}{q} = \frac{kQ}{r^2}$	N/C
Voltage	$U = \frac{W}{q}$	V
Capacitance	$C = \frac{Q}{U}$	F
Parallel plate field	$E = \frac{U}{d}$ Applies when: Uniform fields only; d is measured along the field direction How the real exam asks it	V/m
Ohm's Law	$U = IR$ Applies when: Linear ohmic elements only; non-linear ones need their I–V characteristic curve How the real exam asks it	V
Series resistance	$R = R_1 + R_2 + \cdots$	Ω
Parallel resistance	$\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots$	Ω
Electric power	$P = UI = I^2 R = \frac{U^2}{R}$	W
Joule's Law	$Q = I^2 R t$	J
EMF equation	$\varepsilon = I(R + r)$	V
Ampere force	$F = BIL\sin\theta$ Applies when: A straight current-carrying wire in a uniform field; θ is the angle between wire and field, zero when parallel, direction by the left-hand rule How the real exam asks it	N
Lorentz force	$F = qvB\sin\theta$ Applies when: θ is the angle between velocity and field, zero when v∥B; the force is always perpendicular to the velocity, so it does no work on the particle How the real exam asks it	N
Magnetic flux	$\Phi = BS\cos\theta$	Wb
Faraday's Law	$\varepsilon = -\frac{\Delta\Phi}{\Delta t}$	V
Transformer	$\frac{V_1}{V_2} = \frac{N_1}{N_2}$	-

Waves & Optics

Name	Formula	Unit
Wave speed	$v = f\lambda$	m/s
Period & frequency	$T = \frac{1}{f}$	s
Snell's Law	$n_1 \sin\theta_1 = n_2 \sin\theta_2$	-
Refractive index	$n = \frac{c}{v}$ Applies when: n>1, so light is slower in a medium; n varies with wavelength in the same medium How the real exam asks it	-
Critical angle	$\sin\theta_c = \frac{n_2}{n_1}$	-
Lens formula	$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$	-
Magnification	$m = \frac{v}{u} = \frac{h^{\prime}}{h}$	-

Thermodynamics

Name	Formula	Unit
Heat	$Q = mc\Delta T$	J
Ideal gas law	$pV = nRT$	-
Isothermal	$p_1 V_1 = p_2 V_2$	-
Isobaric	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	-
Isochoric	$\frac{p_1}{T_1} = \frac{p_2}{T_2}$	-
1st Law	$\Delta U = W + Q$ Applies when: W is positive when work is done on the gas, Q positive when heat is absorbed How the real exam asks it	J
Efficiency	$\eta = \frac{W}{Q_1} = 1 - \frac{Q_2}{Q_1}$	-

Modern Physics

Name	Formula	Unit
Photon energy	$E = hf = \frac{hc}{\lambda}$	J
Photoelectric effect	$E_k = hf - W_0$	J
de Broglie wavelength	$\lambda = \frac{h}{p} = \frac{h}{mv}$	m
Mass-energy	$E = mc^2$	J
Nuclear energy	$\Delta E = \Delta m c^2$	J
Half-life	$N = N_0 \left(\frac{1}{2}\right)^{t/T}$	-
Bohr model energy	$E_n = -\frac{13.6}{n^2} \text{ eV}$	eV

Interactive Simulations

Deepen your understanding through visual animations

Newton's Second Law F=ma Interactive Simulation

Adjust force and mass to observe real-time acceleration changes. Visually understand the meaning of F=ma.

F = maa = \frac{F}{m}

5 minBasicInteractive

Kinematics Interactive Simulation

Simulate uniform acceleration motion with synchronized s-t, v-t, a-t graphs. Visually understand kinematics formulas.

s = v_0 t + \frac{1}{2}at^2v = v_0 + at

5 minBasicInteractive

Work & Energy Interactive Simulation

Inclined plane simulation showing real-time conversion of kinetic energy, potential energy, and friction loss.

W = Fs\cos\thetaE_k = \frac{1}{2}mv^2

5 minBasicInteractive

Electrostatics & Coulomb's Law Visualization

Place point charges to observe electric field lines and equipotential lines. Calculate Coulomb force.

F = k\frac{q_1 q_2}{r^2}E = \frac{F}{q}

5 minIntermediateInteractive

DC Circuit Analysis Simulation

Series and parallel circuit visualization with animated current flow. Real-time voltage, current, resistance, and power calculations.

V = IRR_s = R_1 + R_2

5 minBasicInteractive

Circular Motion Interactive Simulation

Visualize uniform circular motion with real-time centripetal force, acceleration, and velocity vectors.

F_c = \frac{mv^2}{r}a_c = \omega^2 r

5 minBasicInteractive

Momentum & Collisions Interactive Simulation

1D two-object collision simulator with elastic and inelastic modes. Visually demonstrate momentum conservation.

p = mvm_1v_1 + m_2v_2 = m_1v_1' + m_2v_2'

5 minBasicInteractive

Geometric Optics Thin Lens Interactive Simulation

Thin lens ray diagram with draggable object. Observe real and virtual image formation and understand imaging rules.

\frac{1}{f} = \frac{1}{u} + \frac{1}{v}M = \frac{v}{u}

5 minBasicInteractive

Wave Motion Interactive Simulation

Transverse wave simulation. Adjust amplitude, wavelength, and frequency. Compare traveling waves and standing waves.

y = A\sin(kx - \omega t)v = f\lambda

5 minIntermediateInteractive

Charged Particle in Magnetic Field Simulation

Simulate charged particle circular motion in uniform magnetic field. Understand Lorentz force.

F = qvBr = \frac{mv}{qB}

5 minIntermediateInteractive

Wave Optics Double-Slit Interference Simulation

Young's double-slit experiment simulation. Adjust slit separation and wavelength to observe interference pattern changes.

d\sin\theta = n\lambda\Delta x = \frac{\lambda L}{d}

5 minIntermediateInteractive

Ideal Gas Law Interactive Simulation

Piston-cylinder model with particle animation showing temperature-pressure relationship. Real-time PV diagram tracing.

PV = nRT\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}

5 minBasicInteractive

First Law of Thermodynamics Interactive Simulation

Energy conservation visualization showing the balance between heat Q, work W, and internal energy change ΔU.

\Delta U = Q - WW = \int P\,dV

5 minIntermediateInteractive

Photoelectric Effect Interactive Simulation

Simulate the photoelectric effect experiment. Adjust light frequency and metal material to observe photoelectron emission conditions.

E_k = h\nu - W_0\nu_0 = \frac{W_0}{h}

5 minIntermediateInteractive

Electromagnetic Induction Interactive Simulation

Simulate a coil moving through a magnetic field region. Real-time magnetic flux and induced EMF graphs. Understand Faraday's law.

\varepsilon = -\frac{d\Phi}{dt}\Phi = BA\cos\theta

5 minIntermediateInteractive

Ready to Practice?

Apply these formulas through practice questions