General Physics Comprehensive Review

QUANTITY AND UNIT

• Physical Quantities: Physical quantities are divided into two types:

  • Base Quantities: These have only one SI unit. Examples include Mass, Length, Time, Current, and Temperature.
  • Derived Quantities: These are expressed by combining suitable base quantities. Examples include Speed, Volume, Area, and Force.

• SI Units (International System of Units):

  • Length: Metre ($m$). Example: $100\,m$.
  • Mass: Kilogram ($kg$). Example: $60\,kg$.
  • Time: Second ($s$). Example: $30\,s$.
  • Current: Ampere ($A$). Example: $15\,A$.
  • Temperature: Kelvin ($K$). Example: $150\,K$.

• Prefixes: Symbols used for multiples or decimals of ten when a quantity is too big or small:

  • Mega ($M$): $10^{6}$ ($1,000,000$). Example: $3\,Mm = 3,000,000\,m$.
  • kilo ($k$): $10^{3}$ ($1,000$). Example: $5\,km = 5,000\,m$.
  • centi ($c$): $10^{-2}$ ($1/100 = 0.01$). Example: $2\,cm = 0.02\,m$.
  • milli ($m$): $10^{-3}$ ($1/1000 = 0.001$). Example: $6\,mm = 0.006\,m$.
  • micro ($\mu$): $10^{-6}$ ($1/1000000 = 0.000001$). Example: $7\,\mu m = 0.000007\,m$.

• Scalar and Vector Definitions:

  • Definition of Scalar: A scalar is a quantity having magnitude only. Examples: mass, length, area, volume, density, time, distance, speed, energy, temperature, current, voltage.
  • Definition of Vector: A vector is a quantity having both magnitude and direction. Examples: weight, displacement, velocity, acceleration, force, moment.

LENGTH AND TIME

• Length Definition: Length is defined as the measurement of something from one end to the other. The SI unit is the metre ($m$).

• Instruments for Measuring Length:

  • Measuring tape: Used for long length; accuracy of $1\,mm$. Examples: Classroom length, building height.
  • Ruler: Used for medium length; accuracy of $1\,mm$. Examples: Paper width, pen length.
  • Vernier calipers: Used for short length; accuracy of $0.1\,mm$. Examples: Pen diameter, internal diameter of a tube.
  • Micrometer screw gauge: Used for very short length; accuracy of $0.01\,mm$. Examples: Hair diameter, razor blade thickness.

• Measuring Protocols:

  • Ruler/Tape: The 0 mark must be at one end. Eyes must be vertically above the mark to avoid parallax error.
  • Vernier Calipers: Outside Jaws measure external dimensions; Inside Jaws measure internal dimensions; the Stem measures depth. Reading is Main Scale (before 0 of vernier) + Vernier Scale (mark in line with main scale).
  • Micrometer Screw Gauge: The object is gripped by turning the Thimble/Ratchet. Reading is Sleeve (Main) scale + Thimble (Circular) scale. Each circular division typically represents $0.01\,mm$.

• Time:

  • SI unit: Second ($s$).
  • Conversion examples:
    • $1\,day = 24\,hours = 1440\,minutes = 86400\,s$.
    • $1\,year = 31536000\,s$.
  • Simple Pendulum: Period ($T$) is defined as the time taken for one complete oscillation.
  • Period Formula: $T = \frac{t}{n}$, where $t$ is total time and $n$ is the number of oscillations.
  • Conclusion: The period depends on the length of the pendulum ($l$) and acceleration due to gravity ($g$). It does not depend on the mass (heavier bob) or amplitude (shorter arc).

SPEED, VELOCITY AND ACCELERATION

• Distance and Displacement Definitions:

  • Distance: Total length taken between two points (Scalar).
  • Displacement: Change of position in a particular direction (Vector).

• Speed and Velocity:

  • Definition of Speed: Rate of change of distance traveled with time (Scalar). $\text{Average Speed} = \frac{\text{Total distance}}{\text{Total time}}$.
  • Definition of Velocity: Rate of change of displacement with time (Vector).

• Acceleration:

  • Definition: Rate of change of velocity with time ($m/s^{2}$).
  • Formula: $a = \frac{v - u}{t}$, where $v$ is final velocity and $u$ is initial velocity.
  • Retardation: Negative acceleration (deceleration) occurs when velocity reduces.

• Equations of Uniformly Accelerated Motion:

  • $v = u + at$
  • $x = ut + \frac{1}{2}at^{2}$
  • $v^{2} = u^{2} + 2ax$

• Acceleration Due to Gravity:

  • Represented by $g \approx 10\,m/s^{2}$. All objects accelerate at this rate toward Earth if air resistance is ignored.
  • Free Fall: Initial velocity $u = 0\,m/s$, acceleration $a = 10\,m/s^{2}$.
  • Vertical Upward Motion: At the top, $v = 0\,m/s$. Acceleration is $-g = -10\,m/s^{2}$.

• Speed-Time Graphs:

  • Gradient: Equals acceleration.
  • Area under graph: Equals total distance traveled.
  • Shapes: Horizontal line (constant speed); Upward sloped line (uniform acceleration); Downward sloped line (uniform deceleration); Curved line (non-uniform acceleration).

MASS AND WEIGHT

• Mass Definition: The quantity of matter in a substance. It remains constant regardless of location. Measured with a Beam Balance in kilograms ($kg$).

• Weight Definition: The attractive force exerted on an object by gravity. It varies with location. Measured with a Spring Balance in Newtons ($N$).

• Weight Formula: $w = mg$.

  • $g$ on Earth is $10\,m/s^{2}$.
  • $g$ on the Moon is $\frac{1}{6}$ of Earth, approximately $1.67\,m/s^{2}$.
  • $g$ in outer space is $0\,m/s^{2}$.

• Centre of Gravity Definition: The point through which a body's whole weight appears to act.

• Stability: The ability of an object to regain its original position after displacement.

  • To increase stability: Lower the centre of gravity and increase the base area.

VOLUME AND DENSITY

• Volume Definition: The amount of space an object occupies. Unit is $m^{3}$ or $cm^{3}$.

• Density Definition: Mass per unit volume.

  • Formula: $D = \frac{m}{V}$. Units: $kg/m^{3}$ or $g/cm^{3}$.

FORCE

• Definition: A pull or a push. It is a vector measured in Newtons ($N$).

• Newton's Laws of Motion:

  • First Law: If forces are balanced, an object at rest stays at rest, and a moving object continues at constant speed in a straight line. This property is Inertia, which depends on mass.
  • Second Law: Unbalanced forces produce acceleration. Force is proportional to acceleration and inversely proportional to mass. Formula: $F = ma$.

• Friction Definition: A force acting to stop the motion of two touching surfaces. It acts in the opposite direction of motion. To reduce friction, use lubricants (oil, grease).

• Centripetal Force: A force directing circular motion towards the centre, at right angles to the motion.

• Hooke's Law: The extension of a loaded spring is directly proportional to the applied load, provided the Elastic Limit is not exceeded.

  • Formula: $\frac{\text{Extension}}{\text{Load}} = \text{Constant}$.

MOMENT

• Definition: The turning effect of a force about a certain point (pivot).

  • Formula: $M = Fd$, where $d$ is the perpendicular distance from the pivot to the line of action of the force.

• Principle of Moments: For a body to be in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about the same point.

WORK, ENERGY AND POWER

• Work Definition: Product of force and distance moved in the direction of the force. Unit: Joule ($J$).

  • Formula: $W = Fd$.

• Energy Definition: The ability to do work.

  • Gravitational Potential Energy (PE): $PE = mgh$.
  • Kinetic Energy (KE): $KE = \frac{1}{2}mv^{2}$.
  • Conservation of Energy: Energy cannot be created or destroyed, only transformed. In free fall, total energy remains constant ($PE + KE = \text{Constant}$).

• Power Definition: Rate of doing work or changing energy.

  • Formula: $P = \frac{W}{t} = \frac{E}{t}$. Unit: Watt ($W$).

SIMPLE MACHINES

• Definition: A device where a force (Effort) applied at one point overcomes a force (Load) at another point.

• Mechanical Advantage (M.A.): $\text{M.A.} = \frac{\text{Load}}{\text{Effort}}$.

• Velocity Ratio (V.R.): $\text{V.R.} = \frac{\text{distance moved by effort } (d_{E})}{\text{distance moved by load } (d_{L})}$.

• Efficiency: $\text{Efficiency} = \frac{\text{Useful work done}}{\text{Total work put in}} \times 100\% = \frac{\text{M.A.}}{\text{V.R.}} \times 100\%$.

THERMAL PHYSICS

• Kinetic Theory:

  • Solid: Particles close together in regular patterns; strong cohesive forces; vibrate at fixed positions.
  • Liquid: Particles close but move vigorously; weaker forces than solids.
  • Gas: Particles far apart; move randomly at high speed; compressible.

• Brownian Motion: The continuous random motion of molecules in fluids observed via smoke particles colliding with invisible air molecules.

• Diffusion Definition: Process by which substances mix due to random molecular motion; moves from high to low concentration.

• Phase Changes: Evaporation is surface-level change at any temperature; Boiling occurs throughout the liquid at a specific Boiling Point. The cooling effect of evaporation occurs because high-energy molecules escape, lowering average KE.

• Thermal Expansion: Materials increase in size when heated. Applications include Bimetallic strips (used in thermostats), rivets (hot fitting), and bridge rollers.

• Thermometry:

  • Mercury: High boiling point ($357^{\circ}C$), silver color, doesn't wet glass, expands uniformly.
  • Alcohol: Low freezing point ($-112^{\circ}C$), safe, expands more than mercury.
  • Clinical Thermometer: Sensitive (large bulb, narrow bore), short range ($35^{\circ}C$ to $42^{\circ}C$), and has a constriction to keep max reading.
  • Fixed Points: Lower Fixed Point ($0^{\circ}C$ for melting ice); Upper Fixed Point ($100^{\circ}C$ for boiling water).

• Gas Laws:

  • Boyle's Law: For constant temperature, $P_{1}V_{1} = P_{2}V_{2}$.
  • Kelvin scale: $T_{K} = T_{C} + 273$. Absolute zero is $0\,K$ or $-273^{\circ}C$.
  • Charles' Law: For constant pressure, $\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$ (using Kelvin).
  • General Gas Equation: $\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}$.

• Thermal Energy Transfer:

  • Conduction: Heat transmission through a medium (solids) via vibrating molecules.
  • Convection: Heat transfer by moving heated particles in fluids (gas/liquids) forming convection currents.
  • Radiation: Flow of heat via infra-red electromagnetic waves; requires no medium. Black/dark surfaces are better absorbers and emitters than shiny/white surfaces.

PROPERTIES OF WAVES

• Wave Types:

  • Transverse: Vibration is at right angles to travel direction (Light, ropes).
  • Longitudinal: Vibration is parallel to travel direction (Sound, springs).

• Wave Terms:

  • Amplitude ($A$): Max displacement from rest.
  • Wavelength ($\lambda$): Distance wave repeats itself.
  • Period ($T$): Time for one oscillation.
  • Frequency ($f$): Waves per second. $f = \frac{1}{T}$.
  • Wave Equation: $v = f\lambda$.

• Sound:

  • Longitudinal wave requiring a medium. Travels faster in solids ($5950\,m/s$ in Iron) than gases ($340\,m/s$ in Air).
  • Pitch: Determined by frequency.
  • Loudness: Determined by amplitude.
  • Audible range: $20\,Hz$ to $20,000\,Hz$.

• Light:

  • Reflection: $\text{Angle of incidence } (i) = \text{Angle of reflection } (r)$. Mirror images are virtual, laterally inverted, same size, and same distance behind.
  • Refraction: Bending of light between media. Snell's Law: $n = \frac{\sin(i)}{\sin(r)}$. Index of water ($1.33$), glass ($1.52$).
  • Critical Angle: The angle of incidence resulting in a $90^{\circ}$ refraction. Total internal reflection occurs if $i > \text{Critical Angle}$.
  • Thin Converging Lens: Thicker at the centre. Terminology: Optical centre ($C$), Principal Axis, Principal focus ($F$), focal length ($f$). Images can be real/virtual and magnified/diminished depending on object distance.

• Electromagnetic Spectrum: All travel at $3 \times 10^{8}\,m/s$. Order: Radio, Micro, IR, Visible, UV, X-ray, Gamma.

ELECTRICITY

• Static Electricity: Caused by rubbing different substances. Like charges repel; unlike attract. Induction is separate charge in an uncharged object.

• Electric Current ($I$): Rate of flow of charge ($Q$). Unit: Ampere ($A$). Formula: $I = \frac{Q}{t}$.

• EMF and PD: Both measured in Volts ($V$). $V = \frac{E}{Q}$. EMF is energy supplied by a cell; PD is energy consumed by a component.

• Resistance ($R$): Opposition to current flow ($\Omega$). Ohm's Law: $R = \frac{V}{I}$.

• Circuits:

  • Series: Same current ($I$); Sum of PDs ($V_{total} = V_{1} + V_{2}$); Sum of resistances ($R_{total} = R_{1} + R_{2}$).
  • Parallel: Current splits ($I_{total} = I_{1} + I_{2}$); Same PD; Reciprocal resistance (1/$R = 1/R_{1} + 1/R_{2}$).

• Practical Electricity:

  • Power: $P = VI$. Cost calculated in kilowatt-hours ($kWh$). $\text{Energy } (kWh) = \text{Power } (kW) \times \text{Time } (h)$.
  • Wire Colors: Live (Brown), Neutral (Blue), Earth (Green/Yellow).
  • Safety Devices: Fuses (prevent fire by melting at specific currents), Earth wire (protects user from shocks), Switches (must be on the Live wire).

MAGNETISM

• Induced Magnetism: Temporary magnetization of materials like iron (Soft - easy to demagnetize) or steel (Hard - holds magnetism).

• Electromagnets: Strength depends on current, number of turns, and core material.

• Electromagnetic Induction: Movement of a conductor in a magnetic field induces an EMF. Lenz's Law: The induced current opposes the motion that creates it.

• Transformers: Devices to vary AC voltage. Formula: $\frac{V_{s}}{V_{p}} = \frac{N_{s}}{N_{p}}$. Ideal transformer: $V_{s}I_{s} = V_{p}I_{p}$.

ELECTRONICS AND ATOMIC PHYSICS

• Electronics: Thermionic emission is electron release from a hot surface. Cathode Ray Oscilloscope (C.R.O.) uses an electron gun and deflection plates to measure voltage and short time intervals.

• Nucleus: Protons ($+$) and Neutrons (neutral) are in the nucleus (nucleons). Electrons ($-$) orbit. Mass number ($A$) = Protons ($Z$) + Neutrons ($N$). Symbol: ${}_Z^A X$.

• Radioactivity:

  • Alpha ($\alpha$): Helium nucleus ($+2$); strong ionizing, weak penetrating.
  • Beta ($\beta$): Electron ($-1$).
  • Gamma ($\gamma$): EM wave (neutral); weak ionizing, strong penetrating.

• Decay Equations:

  • Alpha decay: Atom transforms to ${}_{Z-2}^{A-4}Y$.
  • Beta decay: Atom transforms to ${}_{Z+1}^{A}Y$.

• Half-life: Time for half of the unstable nuclei to decay.