Overview
This lecture covers key topics from several major chapters in physics, including circular and rotational motion, mechanical properties of fluids, kinetic theory of gases, thermodynamics, and simple harmonic motion, focusing on important definitions, formulas, derivations, and concepts for board exam preparation.
Circular & Rotational Motion
- Uniform circular motion (UCM): motion along a circular path with constant angular speed (e.g., satellites).
- Centripetal force acts towards the center; formula: ( F = m v^2/r ) or ( F = m \omega^2 r ).
- Centrifugal force acts away from the center (pseudo force in non-inertial frames).
- Banking of roads increases maximum safe speed on curves.
- Derivation for vehicle speed on banked and horizontal roads depends on friction and road angle.
- Conical pendulum: bob moves in horizontal circle, tension resolved into vertical and horizontal components.
Mechanical Properties of Fluids
- Fluids can flow (liquids & gases); ideal fluids are incompressible with no internal friction.
- Pressure = force/area; SI unit: Pascal (N/m²); acts equally in all directions at a point.
- Pressure in fluids increases with depth (( P = P_0 + \rho gh )).
- Barometer measures atmospheric pressure using mercury column.
- Pascal’s law: pressure applied to enclosed fluid transmits equally in all directions; basis for hydraulic lifts.
- Streamline flow: smooth, orderly motion below critical velocity; above it becomes turbulent.
Viscosity
- Viscous force opposes relative motion between fluid layers; described by Newton’s law of viscosity (( F = \eta \frac{A \Delta v}{\Delta x} )).
- Stoke’s law: viscous drag on sphere ( F = 6 \pi \eta r v ).
- Terminal velocity: constant speed when downward and upward forces on falling sphere balance.
Kinetic Theory of Gases & Thermodynamics
- Ideal gases: large number of tiny, perfectly elastic molecules in random motion.
- Pressure by gases: ( P = \frac{1}{3} \rho v_{rms}^2 ), with ( v_{rms} ) the root mean square velocity.
- Boyle's Law (( PV = ) constant at constant ( T )), Charles’s Law (( V \propto T ) at constant ( P )).
- Internal energy of ideal gas is kinetic energy only.
- Degrees of freedom: monoatomic (3), diatomic (5), polyatomic (6 or more).
- First law of thermodynamics: ( \Delta U = Q - W ).
- Isothermal (constant ( T )), adiabatic (( Q = 0 )), isobaric (constant ( P )), and isochoric (constant ( V )) processes.
- Second law: no heat engine can be 100% efficient.
Simple Harmonic Motion (SHM)
- SHM: restoring force proportional and opposite to displacement (( F = -kx )); acceleration ( a = -\omega^2 x ).
- General solutions: displacement ( x = A \sin(\omega t + \phi) ).
- Time period for simple pendulum: ( T = 2\pi \sqrt{l/g} ).
- Energy in SHM: kinetic and potential energies interconvert, total remains constant.
Key Terms & Definitions
- Centripetal Force — Acts towards the center in circular motion (( F = m v^2/r )).
- Centrifugal Force — Apparent force directed away from center in non-inertial frames.
- Viscosity — Measure of a fluid's resistance to flow.
- Terminal Velocity — Constant velocity when drag force equals net force on falling object.
- Isothermal Process — Thermodynamic process at constant temperature.
- Adiabatic Process — No heat exchange with surroundings.
- Degrees of Freedom — Number of independent ways a molecule can move or store energy.
- Simple Harmonic Motion (SHM) — Periodic motion with force proportional to displacement towards mean position.
Action Items / Next Steps
- Download the New Indian Era app for full PDF notes, formula sheets, and important numericals.
- Revise all formula sheets and previously covered numericals/theories.
- Prepare questions of 2, 3, and 4 marks for upcoming board exams.
- Attend tomorrow’s session for detailed exam question discussions and written solutions.