Physics Fundamentals

Newton's 1st Law (Law of Inertia): A body remains at rest or in uniform motion unless acted upon by an external force. This is why passengers jerk forward when a bus stops suddenly. Newton's 2nd Law: Force = mass x acceleration (F = ma); it defines force quantitatively. Newton's 3rd Law: For every action there is an equal and opposite reaction (e.g., recoil of a gun, rocket propulsion, swimming). Memory aid: '1-Inertia, 2-Force, 3-Reaction'. SI unit of force is Newton (N); 1 N = 1 kg.m/s squared. The 2nd law also gives the concept of momentum (p = mv), and force equals rate of change of momentum.

For uniformly accelerated motion in a straight line, the three equations are: (1) v = u + at, (2) s = ut + (1/2)at squared, (3) v squared = u squared + 2as. Here u = initial velocity, v = final velocity, a = acceleration, t = time, s = distance. For a freely falling body, replace a with g (9.8 m/s squared, often taken as 10). Shortcut: if starting from rest, u = 0, so v = at, s = (1/2)at squared. Distance covered in nth second: s(n) = u + (a/2)(2n - 1). These are heavily tested in numerical problems.

Example 1: A car at 20 m/s brakes with deceleration 5 m/s squared. Stopping distance? Using v squared = u squared + 2as with v = 0: 0 = 400 + 2(-5)s, so s = 40 m. Example 2: A bullet of mass 10 g leaves a 2 kg gun at 400 m/s. By conservation of momentum, gun recoil velocity = (0.01 x 400)/2 = 2 m/s. Tip: In recoil problems, momentum before firing is zero, so (mass of bullet x its velocity) = (mass of gun x recoil velocity). Always convert grams to kilograms before substituting.

Work is done when a force moves a body through a distance: W = Force x Displacement x cos(theta). When force and displacement are in the same direction, W = F x s. SI unit of work and energy is Joule (J); 1 J = 1 N.m. Energy is the capacity to do work. Kinetic energy (KE) = (1/2)mv squared (energy of motion). Potential energy (PE) = mgh (energy due to height). Memory aid: 'KE is for moving, PE is for position'. The Law of Conservation of Energy states energy can neither be created nor destroyed, only transformed from one form to another.

Power is the rate of doing work: Power = Work/Time = W/t. SI unit of power is Watt (W); 1 Watt = 1 Joule/second. Larger units: 1 kilowatt (kW) = 1000 W; 1 Horsepower (HP) = 746 W (approx 0.746 kW). Commercial unit of electrical energy is the kilowatt-hour (kWh) = 1 'unit' = 3.6 x 10^6 J. Shortcut: Energy (kWh) = Power (kW) x Time (hours). Power can also be written as P = Force x velocity. Remember HP is roughly three-quarters of a kilowatt for quick estimation.

Example 1: A body of mass 2 kg moves at 4 m/s. KE = (1/2)(2)(4 squared) = (1/2)(2)(16) = 16 J. Example 2: An object of mass 5 kg is raised to height 10 m (g = 10). PE = mgh = 5 x 10 x 10 = 500 J. Example 3: A 100 W bulb runs for 10 hours daily for 30 days. Energy = (100/1000) kW x 10 x 30 = 30 kWh = 30 units. Tip: For KE problems square the velocity first, then multiply. For electricity, always convert watts to kilowatts by dividing by 1000.

Heat is a form of energy that flows from a hotter to a colder body. Temperature measures the degree of hotness. SI unit of heat is Joule; older unit is calorie (1 cal = 4.2 J). Modes of heat transfer: Conduction (in solids, by contact), Convection (in liquids/gases, by movement of particles), and Radiation (without any medium, like the Sun's heat). Memory aid: 'Con-Con-Rad'. Water has its maximum density at 4 degrees Celsius (anomalous expansion). Boiling point of water is 100 degrees Celsius and freezing point 0 degrees Celsius at normal atmospheric pressure. Kelvin (K) is the SI unit of temperature; 0 degrees C = 273 K.

Light travels in straight lines at speed about 3 x 10^8 m/s in vacuum. Reflection: angle of incidence = angle of reflection. A plane mirror forms a virtual, erect, same-size image. Concave mirror can form real or virtual images (used in torches, headlights, shaving mirrors). Convex mirror always forms a small, virtual image and gives a wide view (used as rear-view mirrors in vehicles). Refraction is bending of light when it passes between media of different densities; it causes a pencil to appear bent in water. A convex lens converges light (used for correcting hypermetropia/long-sightedness); a concave lens diverges light (used for myopia/short-sightedness). White light splits into seven colours (VIBGYOR) through a prism: dispersion.

Sound is a mechanical wave that needs a medium (solid, liquid or gas) to travel; it cannot travel through vacuum. Speed of sound in air is about 340 m/s (at room temperature), faster in water and fastest in solids (steel). An echo is the reflection of sound; to hear a distinct echo the reflecting surface must be at least 17 m away. Audible range for humans is 20 Hz to 20,000 Hz. Below 20 Hz is infrasonic; above 20,000 Hz is ultrasonic (used in SONAR, medical imaging). Memory aid: 'Sound needs a medium; light does not.' Higher frequency means higher pitch; greater amplitude means greater loudness.

Electric current is the flow of charge; its SI unit is the Ampere (A). Ohm's Law states V = IR, where V is voltage (Volt), I is current (Ampere), and R is resistance (Ohm). Memory trick: cover the quantity you need in the V-I-R triangle. Resistances in series add up: R = R1 + R2 + ... For parallel: 1/R = 1/R1 + 1/R2 + ... Electric power P = VI = I squared R = V squared/R. SI unit of power is Watt. A good conductor (copper, silver) has low resistance; an insulator (rubber, glass) has high resistance. Fuse wire has low melting point and protects circuits from overload.

A magnet has two poles: North and South. Like poles repel, unlike poles attract. A freely suspended magnet always points North-South (used in compass). The Earth itself behaves like a giant magnet. An electric current produces a magnetic field around it (Oersted's discovery); this is the principle of the electromagnet and electric motor. A coil carrying current behaves like a bar magnet (solenoid). Magnetic substances: iron, cobalt, nickel. Memory aid for magnetic metals: 'I Co Ni' (Iron, Cobalt, Nickel). The unit of magnetic flux density is Tesla. An electric generator (dynamo) converts mechanical energy to electrical energy using electromagnetic induction.

Example 1: A 6 V battery drives a current of 2 A through a resistor. Resistance R = V/I = 6/2 = 3 Ohm. Example 2: Two resistors of 3 Ohm and 6 Ohm in series: total R = 3 + 6 = 9 Ohm. In parallel: 1/R = 1/3 + 1/6 = 3/6, so R = 2 Ohm (parallel resistance is always less than the smallest resistor). Example 3: Power of a device drawing 5 A at 220 V: P = VI = 220 x 5 = 1100 W. Tip: In series, current is the same; in parallel, voltage is the same. Always check whether the question asks for series or parallel.