Physics numericals become dramatically faster once the underlying formulas are organized by the situation they describe, rather than memorized as an isolated list. This guide groups the essential formulas by chapter, with a short note on when and why each one applies — exactly how they show up in board and O/A-Level exams.
Mechanics
Newton’s laws in formula form:
- F = ma (net force equals mass times acceleration)
- Every action has an equal and opposite reaction (no formula, but frequently tested conceptually)
Kinematics equations (constant acceleration):
- v = u + at
- s = ut + ½at²
- v² = u² + 2as
Here u is initial velocity, v is final velocity, a is acceleration, t is time, and s is displacement. These three equations solve almost every straight-line motion problem — the skill is identifying which three variables are given and picking the equation that uses them.
Projectile motion: Split velocity into horizontal (constant) and vertical (affected by gravity) components. Horizontal distance = horizontal velocity × time; vertical motion follows the standard kinematics equations with a = g (9.8 m/s² downward).
Work, energy, and power:
- Work = Force × displacement × cos θ (θ is the angle between force and displacement)
- Kinetic energy = ½mv²
- Gravitational potential energy = mgh
- Power = Work ÷ time
Circular motion: Centripetal force = mv²/r, always directed toward the center of the circular path — a frequent point of confusion is forgetting this force doesn’t do work, since it’s always perpendicular to velocity.
Electromagnetism
Ohm’s law and circuits:
- V = IR (voltage = current × resistance)
- Series circuits: total resistance = R₁ + R₂ + R₃…
- Parallel circuits: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃…
- Power = VI = I²R = V²/R
Coulomb’s law: F = kq₁q₂/r², describing the force between two point charges — the force decreases with the square of the distance, which is why doubling the distance reduces the force to a quarter of its original value.
Magnetic force on a current-carrying wire: F = BIL sin θ, where B is magnetic field strength, I is current, L is wire length, and θ is the angle between the wire and the field. The right-hand rule determines the direction — a frequently tested conceptual point separate from the calculation itself.
Electromagnetic induction: EMF = −N(ΔΦ/Δt), where N is the number of coil turns and ΔΦ/Δt is the rate of change of magnetic flux. The negative sign (Lenz’s law) indicates the induced current opposes the change that created it — a concept examiners test by asking for the direction of induced current, not just its magnitude.
Waves and Optics
Wave equation: v = fλ (speed = frequency × wavelength), the single most-used formula across sound and light wave questions.
Reflection and refraction:
- Angle of incidence = angle of reflection (law of reflection)
- Snell’s law: n₁ sin θ₁ = n₂ sin θ₂ (refraction between two media)
Lens and mirror formula: 1/f = 1/v + 1/u, where f is focal length, v is image distance, and u is object distance. Sign conventions (real vs. virtual images, concave vs. convex) are where most marks are lost — always draw a ray diagram first to confirm the sign of each value before substituting.
Magnification: m = v/u = height of image / height of object.
Modern Physics (FSc Part 2 / A-Level)
Photoelectric effect: Einstein’s equation, E = hf = φ + KE_max, where hf is the energy of an incoming photon, φ is the work function of the material, and KE_max is the maximum kinetic energy of the ejected electron. A common exam angle: no electrons are emitted below the threshold frequency, regardless of light intensity — a conceptual point that trips up students who think intensity alone should matter.
Mass-energy equivalence: E = mc², rarely used for direct calculation in board exams but frequently tested conceptually in questions about nuclear reactions and binding energy.
Units and Constants Worth Memorizing
- Acceleration due to gravity, g ≈ 9.8 m/s² (or 10 m/s² for quick estimates)
- Speed of light, c ≈ 3 × 10⁸ m/s
- Planck’s constant, h ≈ 6.63 × 10⁻³⁴ J·s
- Always express final answers in SI units unless the question specifies otherwise
Exam Technique Notes
- Draw a diagram before writing any formula. A free-body diagram for mechanics, a ray diagram for optics, or a circuit diagram for electromagnetism forces you to correctly identify every variable in the problem before calculating anything.
- Check units with dimensional analysis. If your final answer’s units don’t make physical sense (like getting an area for a question asking for a distance), you’ve made an error somewhere in the calculation.
- Distinguish scalar and vector quantities. Direction matters in mechanics and electromagnetism — dropping a negative sign or ignoring direction changes the entire meaning of an answer.
- State assumptions in word problems. Many mechanics problems assume no air resistance or a frictionless surface — stating that assumption explicitly is often part of the expected answer.
Frequently Asked Questions
Which physics formulas are used most across different chapters? The kinematics equations (v = u + at, s = ut + ½at², v² = u² + 2as) and F = ma appear, directly or indirectly, across mechanics, projectile motion, and even some electromagnetism problems involving charged particles.
How do I remember which sign convention to use in the lens formula? Draw the ray diagram first — a real image gets a positive value, a virtual image gets a negative value, and the diagram will visually confirm which applies before you touch the formula.
Is calculus needed for FSc/A-Level physics? Basic differentiation and integration appear in some derivations (like deriving kinematics equations from first principles) but most numerical problems can be solved with the standard formulas above without calculus.
What’s the most commonly forgotten step in electromagnetism numericals? Converting units before substituting — especially resistance in ohms, current in amps, and power in watts — mixing units is one of the most common sources of wrong answers.