Physics Fundamentals for Competitive Exams

Base quantities are chosen independently within a measurement system. Derived quantities are defined using combinations of other quantities.

In the International System of Units (SI), length, mass and time are base quantities. Their units are the metre, kilogram and second.

Velocity describes the rate of change of displacement. Its unit is metres per second, so velocity is a derived quantity.

Acceleration describes the rate of change of velocity. Its unit is m/s². A velocity unit and an acceleration unit are not interchangeable.

A force is a push or pull arising from an interaction. It has both magnitude and direction.

A force can change an object’s speed, direction or shape. Several forces can act on one object together.

The net force is their vector sum. Equal opposite forces on the same object can balance, leaving zero net force.

• Contact forces: friction and muscular pushes involve physical contact.
• Field forces: gravity, electric forces and magnetic forces can act across a distance.

A book resting on a table still experiences forces. Its upward support and downward weight can balance. Rest does not mean that every force is absent.

Newton’s first law describes motion when the net external force is zero. An object then remains at rest or continues with constant velocity.

The law applies in an inertial frame. This is a reference frame in which a free object has no acceleration.

Inertia is resistance to a change in velocity. A moving object does not need a forward force merely to keep moving at constant velocity.

Why does a sliding object stop? Friction can provide an opposing net force. The object slows because of that interaction.

Seatbelt example. During sudden braking, your body tends to continue moving forward. The seatbelt supplies a force that slows your body with the car.

For a constant-mass object in an inertial frame, Fₙₑₜ = ma.

• Fₙₑₜ: net external force, measured in newtons, or N.
• m: mass, measured in kilograms, or kg.
• a: acceleration, measured in m/s².

At fixed mass, a larger net force produces greater acceleration. At fixed net force, a larger mass produces smaller acceleration.

Worked example. A 2 kg object experiences a net force of 10 N.

a = Fₙₑₜ/m = 10/2 = 5 m/s².

A push of 10 N does not guarantee that acceleration if an opposing force also acts. Use the resultant force after including all forces.

One newton equals 1 kg·m/s². A net force of 1 N on 1 kg produces 1 m/s².

The formula gives acceleration, not speed. Finding a later speed also requires the starting velocity and suitable time information.

Newton’s third law describes a pair of forces in one interaction. The forces have equal magnitudes and opposite directions.

The forces act simultaneously on different objects. One force is not a delayed response caused by the other force.

When your hand pushes a wall, the wall pushes your hand. The force on the wall and force on your hand belong to different force diagrams.

They therefore do not cancel in the net force on either object individually. Balanced forces on one object are a different comparison.

Galileo Galilei helped develop ideas about inertia and motion. His work challenged the assumption that motion always requires a continuing driving force.

Isaac Newton presented his three laws in 1687. The book was Philosophiæ Naturalis Principia Mathematica, commonly called the Principia.

The laws describe ordinary classical motion. Their simple forms need different treatment for relativistic motion and quantum phenomena.

Momentum is mass multiplied by velocity: p = mv. Its unit is kg·m/s, and its direction follows velocity.

A system’s total momentum stays constant when its net external force is zero. During a brief collision, conservation can be approximated when external impulse is negligible.

The system must include every interacting object relevant to the calculation. A single object’s momentum can change while the system’s total stays unchanged.

Recoil example. Firing sends the bullet forward and the gun backward. In the isolated-system model, their momentum changes are equal and opposite.

Equal momentum magnitudes do not imply equal speeds. The much heavier gun has a smaller recoil speed.

Temperature describes thermal state and helps determine the direction of spontaneous heat transfer. Heat is energy transferred because of a temperature difference.

Net spontaneous heat transfer goes from a hotter body towards a cooler body. An object contains internal energy; it does not contain heat as a stored substance.

Tea and bath example. A small cup of tea can be hotter than a large lukewarm bath. Temperature alone does not compare their total internal energies.

A clearer comparison asks how much energy heats each water sample through the same temperature rise. With the same specific heat, the larger mass needs more energy.

For heating without a phase change, Q = mcΔT when specific heat is effectively constant.

• Q: transferred energy, measured in joules.
• m: sample mass, measured in kilograms.
• c: specific heat, measured in J/(kg·K).
• ΔT: temperature change, measured in kelvins or Celsius degrees.

Can a hot spark start a fire? A small hot particle can transfer relatively little energy because of its small mass. However, a spark can still ignite suitable fuel. High temperature alone does not determine the outcome.

Sound is a mechanical disturbance travelling through matter. Air, water and solids can carry sound.

In air, neighbouring particles transmit alternating compressions and rarefactions. The particles vibrate locally while the disturbance travels.

A vacuum has no material particles to transmit that mechanical disturbance. Sound therefore cannot propagate through an ideal vacuum.

Light can cross a vacuum because it is an electromagnetic wave. An explosion’s light may be seen across space without its sound crossing the intervening vacuum.

Electric current is the rate at which charge passes a point. It is measured in amperes.

A conductor allows charge to move readily. An insulator strongly restricts ordinary charge movement.

Metals are common conductors. Rubber, plastic and dry wood are common insulating materials. An insulator does not block every possible current under every condition.

For a simple steady battery circuit, a closed conducting path connects the terminals through the load. Opening a switch interrupts that path.

This describes ordinary steady conduction in the simple circuit. It does not mean that every electrical phenomenon requires the same two-terminal loop.

Conventional current follows the direction positive charge would move. In an external battery circuit, it runs from the positive terminal towards the negative terminal.

Electrons drift in the opposite direction in metal wires because their charge is negative. In liquids, mobile positive and negative ions can also carry current.

Current direction is therefore a convention about charge movement. It is not a rule that every material contains only moving electrons.

For an ohmic conductor under unchanged physical conditions, voltage is proportional to current. Temperature must remain suitably constant.

The relationship is V = IR.

• V: potential difference, in volts.
• I: current, in amperes.
• R: resistance, in ohms.

Worked example. Across a 4 Ω resistor, the potential difference is 12 V.

I = V/R = 12/4 = 3 A.

Resistance is not necessarily constant in every component. A hot filament can change resistance as its temperature changes.

Current through a resistive element transfers electrical energy into thermal energy. This effect operates in heater elements and lamp filaments.

Nichrome resistance alloy is used in heating elements.

For a constant current, the heating power is P = I²R. Increasing resistance increases power only when current stays fixed.

At fixed voltage, P = V²/R instead. Increasing resistance then reduces power. Always identify which quantity stays fixed.

A fuse opens a circuit by melting its element under specified overcurrent conditions. Its operation depends on both current magnitude and duration.

The fuse is selected to carry the intended load while protecting the circuit. It does not always melt instantly when current first exceeds its printed rating.

Mobile ions carry electric charge through many solutions. Pure distilled water is a poor conductor compared with many ionic solutions.

Dissolving a suitable acid, base or salt can supply mobile ions. Conductivity depends on the substance and its concentration. Not every dissolved substance makes water a good conductor.

Electroplating uses electric current to deposit a metal coating on a conducting object. Metal ions gain electrons at the object’s surface and become metal atoms.

Examples include gold or silver coatings on jewellery. Tin coatings are used on food cans. Zinc or chromium coatings can help protect iron surfaces.

The usefulness of the coating depends on the metal and the application. Electroplating does not mean that every metal coating offers identical protection.

Rubbing suitable materials can transfer electrons between them. One object can become negatively charged while the other becomes positively charged.

Like charges repel; unlike charges attract. Rubbing redistributes charge rather than creating a net charge from nothing.

Earthing provides a conducting connection with Earth. Charge can flow between the object and Earth, reducing excess charge under suitable conditions.

A lightning protection system provides a conducting route for a lightning discharge. The system directs the discharge towards its grounding network.

A lightning conductor does not prevent all lightning strikes. Its purpose is to reduce damage through an appropriate discharge path.

Benjamin Franklin’s 1752 experiments helped establish that lightning is electrical. Lightning and small electrical sparks both involve electrical discharge.

Georg Ohm published his circuit theory in 1827. His work related current, potential difference and resistance through experimental and mathematical investigation.

Recognition of Ohm’s work included the Royal Society’s Copley Medal in 1841. The resistance unit, the ohm, carries his name.

Light shows both wave behaviour and quantised energy exchange. These descriptions explain different observations.

Reflection changes light’s direction at a surface. Refraction changes its direction when it crosses materials under suitable conditions.

Dispersion separates colours because different wavelengths can refract by different amounts. A prism provides a familiar example.

Wave behaviour also includes interference and diffraction. In the photoelectric effect, light exchanges energy in packets called photons.

A photon is not a tiny classical ball following every ordinary mechanical rule. Wave–particle duality describes the evidence from both kinds of experiment.

The electromagnetic spectrum groups electromagnetic radiation by wavelength and frequency. From longer to shorter wavelengths, the usual order is:

Radio → microwaves → infrared → visible → ultraviolet → X-rays → gamma rays.

As wavelength decreases, frequency increases. A photon’s energy increases with frequency.

All electromagnetic waves travel at the same speed in a vacuum. Shorter wavelength does not mean a faster vacuum speed.

Visible light is the small band normally detected by human vision. Radio waves, microwaves and infrared are not ordinary visible colours.

William Herschel discovered infrared radiation in 1800. He used a prism to separate sunlight into colours.

Thermometers measured heating in different parts of the spectrum. A thermometer beyond the red end showed heating where no visible colour appeared.

The experiment revealed invisible radiation beyond visible red. The result connected an invisible part of the spectrum with measurable heating.

Infrared remote controls emit infrared signals. Thermal cameras detect infrared emitted by objects.

Some night-vision devices use infrared. Night vision does not always use the same technology.

Iron, nickel and cobalt are familiar ferromagnetic materials under suitable conditions. Ordinary magnets strongly attract these materials.

Wood, plastic and rubber are not normally strongly attracted to an ordinary magnet. This everyday description does not mean that every material lacks every magnetic response.

Magnetite is an iron-oxide mineral and an important iron ore. Naturally magnetised magnetite, called lodestone, can act as a natural magnet.

An ordinary bar magnet has north and south poles. Like poles repel; unlike poles attract.

A freely turning compass needle aligns with the local magnetic field. Its north-seeking end indicates magnetic north under ordinary compass conditions.

Magnetic north can differ from geographic north. Nearby magnets or current-carrying wires can also alter the needle’s direction.

An electric current produces a magnetic field. A compass beside a current-carrying wire can reveal that field through its deflection.

A changing magnetic flux through a circuit induces an electromotive force, or induced voltage. Flux depends on the field and how the circuit spans it.

An induced current flows when the circuit provides a suitable closed conducting path. A changing field does not guarantee a current through an open circuit.

An electric motor uses magnetic forces on current-carrying parts to produce motion. It converts electrical energy into mechanical energy.

A generator uses electromagnetic induction to convert mechanical energy into electrical energy. Energy comes from the driving input; magnetism does not supply energy without an input.

In April 1820, Hans Christian Oersted observed a compass deflection near a current-carrying wire. He reflected on the observation for three months before conducting further experiments.

Oersted published the findings in July 1820. The observation showed that electric current could produce a magnetic effect.

The result helped connect electricity and magnetism. It did not by itself establish the complete modern theory of electromagnetism.

Choose the physical quantity and conditions before using a formula. Force divided by mass gives acceleration, rather than speed.

• Central Armed Police Forces (CAPF) Assistant Commandants (ACS), 2018, Q59: sound needs a material medium; light can cross a vacuum. View this question on the full CAPF ACS 2018 paper →
• Combined Defence Services (CDS) II, 2018, Q18: visible light is the spectrum band normally detected by the human eye. View this question on the full CDS-II 2018 paper →
• CAPF ACS 2020, Q6: action and reaction are simultaneous forces on different objects.
• National Defence Academy–Naval Academy (NDA–NA) II, 2016, Q81: a net force of 1 N on 1 kg gives 1 m/s². View this question on the full NDA-NA-II 2016 paper →

For third-law questions, distinguish the paired interaction from forces balancing on one body. For acceleration questions, identify the net external force.