Comprehensive Physics University Physics Study Guide: Mechanics to Modern Physics

PHYSICS OVERVIEW AND CAREERS

• Definition of Physics: Physics is the branch of science that deals with matter in relation to energy.
• Matter: Anything that occupies space and has weight. It exists in three states: Solids, Liquids, and Gases.
• Energy: The ability to do work. Forms include Heat, Sound, Light, Chemical, Solar, Nuclear, and Mechanical (Kinetic and Potential).
• Career Opportunities: Electrical engineering, Civil engineering, Architecture, Mechanical engineering, Geology, Chemical engineering, Astronomy, Information technology, Telecom engineering, Teaching, Medicine, Pharmacy, Petroleum engineering.
• Branches of Physics: Mechanics, Optics (light and waves), Heat, Electricity (Electrostatics and Current), Magnetism, and Modern Physics.

MEASUREMENTS AND UNITS

• SI Units: The System International of Units; internationally agreed-upon measurements.
• Basic (Fundamental) Quantities: Quantities that cannot be expressed in terms of others.
    - Length: Metre ($m$)
    - Time: Seconds ($s$)
    - Mass: Kilograms ($kg$)
    - Electric Current: Ampere ($A$)
    - Temperature: Kelvin ($K$)
    - Amount of Substance: Mole ($M$)
• Derived Quantities: Expressed in terms of basic quantities. Examples:
    - Volume ($m^3$), Density ($kg\,m^{-3}$), Area ($m^2$), Weight/Force (Newton, $N$), Speed/Velocity ($m\,s^{-1}$), Acceleration ($m\,s^{-2}$), Power (Watts, $W$), Work/Energy (Joules, $J$), Pressure ($N\,m^{-2}$ or Pascal, $Pa$).

LENGTH AND MEASURING INSTRUMENTS

• Length: Distance between two points. $1\,km = 1000\,m$, $1\,m = 100\,cm$, $1\,m = 1000\,mm$.
• Vernier Caliper:
    - Used for short distances ($1\,cm$ to $10\,cm$) and diameters.
    - Main scale in $cm$; Vernier scale in $mm$ (10 divisions).
    - Reading = Main scale value + (Vernier scale division coinciding with main scale/100).
• Micrometer Screw Gauge:
    - Measures very small lengths (e.g., wire diameter, paper thickness) with accuracy of $0.01\,mm$.
    - Reading = Sleeve scale value + Thimble scale value coinciding with datum line.
• Metre Rule: Graduated in $cm$ or $mm$. Essential to avoid parallax error by positioning eye perpendicularly above the scale.

MASS, WEIGHT, AND DENSITY

• Mass: Quantity of matter. Constant everywhere. Measured in $kg$, $g$, or tonnes.
• Weight: Gravitational pull acting on a body towards the center of the Earth. Varies with location. Units: Newtons ($N$).
    - Formula: $W = m \times g$ (where $g \approx 10\,m\,s^{-2}$ on Earth).
• Density ($\rho$): Mass per unit volume.
    - Formula: $\rho = \frac{m}{V}$. SI unit: $kg\,m^{-3}$.
    - Factors affecting density: Temperature (inverse), Pressure (direct for gases), Concentration of atoms, Change of state.
• Relative Density (R.D): Ratio of density of substance to density of water. No units.
    - $R.D = \frac{\text{Density of substance}}{\text{Density of water}}$ or $\frac{\text{Mass of substance}}{\text{Mass of equal volume of water}}$.

FORCE AND MOTION

• Force: A push or pull changing a body's state of rest or motion. Unit: Newton ($N$).
• Newton's Laws of Motion:
    - 1st Law (Inertia): Body remains at rest or uniform motion unless acted on by external force.
    - 2nd Law: Rate of change of momentum is proportional to applied force ($F = ma$).
    - 3rd Law: For every action, there is an equal and opposite reaction.
• Resultant Force: Single force with same effect as multiple forces.
    - Same direction: Add forces ($F_1 + F_2$).
    - Opposite direction: Subtract forces ($F_1 - F_2$).
    - Right angles: Pythagoras theorem ($\sqrt{F_1^2 + F_2^2}$).
• Friction: Opposes relative motion.
    - Static: Between stationary bodies; depends on coefficient of friction ($\mu$) and Normal reaction ($R$). $F = \mu \times R$.
    - Dynamic: Between moving bodies.
• Momentum ($p$): Product of mass and velocity ($p = mv$).
    - Conservation of Momentum: Total momentum before collision = Total momentum after collision ($m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$).

WORK, ENERGY, AND POWER

• Work: Force times distance moved in direction of force ($W = F \times d$). Unit: Joule ($J$).
• Kinetic Energy (K.E): Energy due to motion ($K.E = \frac{1}{2}\,m\,v^2$).
• Potential Energy (P.E): Energy due to position ($P.E = m\,g\,h$).
• Law of Conservation of Energy: Energy cannot be created or destroyed, only transformed.
• Power: Rate of doing work. Unit: Watt ($W$).
    - Formula: $P = \frac{W}{t} = F \times v$.

PRESSURE

• Pressure ($P$): Force acting normally per unit area.
    - Formula: $P = \frac{F}{A}$. Unit: Pascal ($Pa$ or $N\,m^{-2}$).
• Pressure in Liquids: Increases with depth ($h$), density ($\rho$), and gravity ($g$).
    - Formula: $P = h\,\rho\,g$.
    - Pascal's Principle: Pressure applied to enclosed fluid is transmitted equally.
• Atmospheric Pressure: Exerted by weight of air. Measured using Barometers.
    - Standard atmospheric pressure $\approx 760\,mmHg$ or $103,360\,N\,m^{-2}$.

MECHANICAL PROPERTIES OF MATERIALS

• Strength: Ability to withstand force before breaking.
• Stiffness: Resistance to change of size/shape.
• Ductility: Ability to be stretched/rolled without breaking (e.g., metals).
• Brittleness: Snaps after elastic limit is reached (e.g., glass).
• Elasticity: Regains shape after force removal (Hooke's Law).
• Hooke’s Law: Force ($F$) is proportional to extension ($e$) within elastic limit. $F = k \times e$.
• Young's Modulus: Ratio of Tensile Stress ($\frac{F}{A}$) to Tensile Strain ($\frac{e}{L}$).

MACHINES

• Definitions:
    - Load ($L$): Force to overcome.
    - Effort ($E$): Force applied.
    - Mechanical Advantage: $M.A = \frac{L}{E}$.
    - Velocity Ratio: $V.R = \frac{\text{Effort Distance}}{\text{Load Distance}}$.
    - Efficiency ($\eta$): $\eta = \frac{M.A}{V.R} \times 100\%$.
• Types: Levers (1st, 2nd, 3rd class), Pulleys, Inclined Plane, Wheel and Axle, Gears, Screws, Hydraulic Press.

HEAT MEASUREMENT AND GAS LAWS

• Specific Heat Capacity ($c$): Heat needed to raise $1\,kg$ by $1\,K$. $Q = m\,c\,\Delta\theta$.
• Latent Heat ($L$): Heat needed to change state without temperature change. $Q = m\,L$.
    - Fusion: Solid to Liquid.
    - Vaporization: Liquid to Gas.
• Gas Laws:
    - Boyle's Law: $P_1V_1 = P_2V_2$ (Constant Temperature).
    - Charles' Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (Constant Pressure).
    - Pressure Law: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ (Constant Volume).
    - Combined Gas Equation: $\frac{PV}{T} = \text{Constant}$.

LIGHT AND OPTICS

• Reflection: Angle of incidence ($i$) = Angle of reflection ($r$).
• Refraction (Snell's Law): $\frac{\sin(i)}{\sin(r)} = n$ (Refractive Index).
• Curved Mirrors and Lenses:
    - Concave mirror: Converging.
    - Convex mirror: Diverging (wide field of view).
    - Convex lens: Magnifies images when object is between $F$ and $O$.
• Total Internal Reflection: Occurs when light moves from denser to less dense medium at an angle greater than critical angle ($C$).
    - $\sin(C) = \frac{1}{n}$.

WAVES AND SOUND

• Wave Equation: $V = f\,\lambda$ (Velocity = Frequency × Wavelength).
• Transverse Waves: Vibration perpendicular to direction of travel (e.g., Light).
• Longitudinal Waves: Vibration parallel to direction of travel (e.g., Sound).
• Sound: Needs a material medium. Speed in air $\approx 330\,m\,s^{-1}$.
    - Echo: Reflected sound. Distance $D = \frac{V \times t}{2}$.

ELECTRICITY AND MAGNETISM

• Ohm's Law: $V = I \times R$ (Voltage = Current × Resistance).
• Resistors:
    - Series: $R_{total} = R_1 + R_2 + R_3$
    - Parallel: $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$
• Transformers: $\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s}$ (for 100% efficiency).
• Magnetism: Like poles repel; unlike poles attract. Soft iron (temporary magnets), Steel (permanent magnets).

MODERN PHYSICS

• Atomic Structure: Protons and Neutrons in nucleus; Electrons in orbits.
• Radioactivity: Spontaneous decay of unstable nuclei. Emissions:
    - Alpha ($\alpha$): Helium nucleus, low penetration, high ionization.
    - Beta ($\beta$): Fast electron, medium penetration.
    - Gamma ($\gamma$): Electromagnetic radiation, high penetration, no charge.
• Half-Life ($T_{1/2}$): Time for half the radioactive atoms to decay.
• Nuclear Reactions:
    - Fission: Splitting a heavy nucleus (used in reactors).
    - Fusion: Combining light nuclei (occurs in stars).