Physics Formula Sheet: What to Memorise vs What to Derive

Every Class 11 and 12 science student faces the same panic right before a physics exam: staring at a 50-page formula notebook and wondering how on earth anyone is supposed to remember all of it. Between CBSE, ICSE, state boards, JEE Main, and NEET, the sheer volume of equations in mechanics, electromagnetism, and modern physics is staggering.

The secret that top rankers and seasoned educators know is that you are not actually supposed to memorise all of them. Memorising every single variation of a formula is a trap. It leads to cognitive overload, formula confusion in the exam hall, and total paralysis when a question is framed slightly differently.

To survive and score high in the 2026-27 academic session, you need a triage system. Let us sort your physics syllabus into two distinct piles: things you must commit to long-term memory, and things you must learn to derive in under 30 seconds.

The Core Memory Bank: What to Memorise Permanently

Some formulas appear so frequently, or form the foundational bedrock of so many complex problems, that stopping to derive them during a 3-hour exam or a high-speed JEE/NEET paper will cost you precious time. Memorise these verbatim, along with their sign conventions and validity conditions.

1. Fundamental Definitions and Laws

These cannot be derived because they are axioms or experimental observations.

• Coulomb's Law: $F = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r^2}$
• Biot-Savart Law: $d\vec{B} = \frac{\mu_0}{4\pi} \frac{I d\vec{l} \times \hat{r}}{r^2}$
• Faraday's Law of Induction: $\varepsilon = -\frac{d\Phi_B}{dt}$

2. High-Frequency Shortcuts for Competitive Exams

These are derived from longer calculus steps, but having them on immediate recall gives you a massive speed advantage in objective papers.

• Time period of a physical pendulum: $T = 2\pi \sqrt{\frac{I}{mgd}}$
• Radius of $n^{\text{th}}$ Bohr orbit: $r_n = 0.529 \frac{n^2}{Z} \, \text{Å}$
• Root mean square speed of gas molecules: $v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$

3. Standard Integrals and Constants

Never waste time trying to remember the value of permittivity of free space ($\varepsilon_0$), Planck's constant ($h$), or standard trigonometric limits used in wave optics. Keep these permanently etched in your brain.

| Constant / Term | Standard Value / Expression | Where to Use | | :--- | :--- | :--- | | Permittivity ($\varepsilon_0$) | $8.85 \times 10^{-12} \, \text{C}^2\text{N}^{-1}\text{m}^{-2}$ | Electrostatics, Capacitance | | Planck's Constant ($h$) | $6.63 \times 10^{-34} \, \text{JS}$ | Dual Nature, Atomic Structure | | Rydberg constant ($R$) | $1.097 \times 10^7 \, \text{m}^{-1}$ | Hydrogen spectrum calculations |

The Derivation Zone: What Never to Memorise

If you find yourself trying to memorise formulas involving lengthy algebraic expansions or multiple substitution steps, stop immediately. If you understand the underlying principle, you can recreate these equations on your rough sheet in seconds. Memorising them is a waste of mental bandwidth.

1. Kinematic Equations via Calculus

Instead of memorising motion formulas for variable acceleration, remember the definitions: $v = \frac{dx}{dt}$ and $a = \frac{dv}{dt}$. If acceleration is constant, basic integration yields: $v = u + at, \quad s = ut + \frac{1}{2}at^2, \quad v^2 = u^2 + 2as$ If you forget these, re-integrating takes ten seconds and guarantees you haven't mixed up a plus or minus sign.

2. Moment of Inertia Variations

Do not memorise the moment of inertia for every odd axis of every shape. Memorise only two standard results:

• Rod about center: $I = \frac{ML^2}{12}$
• Ring/Cylinder about axis: $I = MR^2$
• Disc/Solid Cylinder about axis: $I = \frac{1}{2}MR^2$

For everything else (like a rod about its end, or a disc about a tangent), apply the Parallel Axis Theorem ($I = I_{\text{cm}} + md^2$) or Perpendicular Axis Theorem ($I_z = I_x + I_y$).

3. Optics and Electrostatic Field Variations

In ray optics and electrostatics, standard geometries have specific derivations.

• Mirror/Lens Formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{v}$ (or minus for lenses). Instead of memorising sign permutations for real vs virtual images, draw a quick ray diagram and apply coordinate geometry sign conventions on the spot.
• Electric field due to an infinite sheet or ring: Derive these using Gauss's Law ($\oint \vec{E} \cdot d\vec{A} = \frac{q_{\text{enclosed}}}{\varepsilon_0}$) or direct integration. Knowing how to set up the symmetry saves you when a question introduces a non-standard charge distribution.

Quick Checklist for Your Formula Notebook

Before you finalise your physics formula sheets for board exams or entrance tests, run them through this filter:

• [ ] Can I explain where this formula comes from? If yes, keep it in your derivation practice log.
• [ ] Does it save me $\ge$ 45 seconds in a numerical problem? If yes, add it to your memorisation flashcards.
• [ ] Are the dimensional formulas verified? Always check if both sides match.
• [ ] Do I know the boundary conditions? (e.g., Is this valid only for small angles $\theta \ll 1$? Is this formula only for adiabatic processes?)

Mastering physics isn't about how many formulas fit inside your head. It is about knowing how a few fundamental laws build everything else. Build your sheet wisely, practice your derivations, and keep your prep sharp with Edumath.