Topics
Physical World and Measurement
Physical World
Units and Measurements
- International System of Units
- Measurement of Length
- Measurement of Mass
- Measurement of Time
- Accuracy, Precision and Least Count of Measuring Instruments
- Errors in Measurements
- Significant Figures
- Dimensions of Physical Quantities
- Dimensional Formulae and Dimensional Equations
- Dimensional Analysis and Its Applications
- Need for Measurement
- Units of Measurement
- Fundamental and Derived Units
- Length, Mass and Time Measurements
- Introduction of Units and Measurements
Motion in a Straight Line
- Position, Path Length and Displacement
- Average Velocity and Average Speed
- Instantaneous Velocity and Speed
- Kinematic Equations for Uniformly Accelerated Motion
- Acceleration (Average and Instantaneous)
- Relative Velocity
- Elementary Concept of Differentiation and Integration for Describing Motion
- Uniform and Non-uniform Motion
- Uniformly Accelerated Motion
- Position-time, Velocity-time and Acceleration-time Graphs
- Position - Time Graph
- Relations for Uniformly Accelerated Motion (Graphical Treatment)
- Introduction of Motion in One Dimension
- Motion in a Straight Line
Kinematics
Motion in a Plane
- Scalars and Vectors
- Multiplication of Vectors by a Real Number or Scalar
- Addition and Subtraction of Vectors - Graphical Method
- Resolution of Vectors
- Vector Addition – Analytical Method
- Motion in a Plane
- Motion in a Plane with Constant Acceleration
- Projectile Motion
- Uniform Circular Motion (UCM)
- General Vectors and Their Notations
- Motion in a Plane - Average Velocity and Instantaneous Velocity
- Rectangular Components
- Scalar (Dot) and Vector (Cross) Product of Vectors
- Relative Velocity in Two Dimensions
- Cases of Uniform Velocity
- Cases of Uniform Acceleration Projectile Motion
- Motion in a Plane - Average Acceleration and Instantaneous Acceleration
- Angular Velocity
- Introduction of Motion in One Dimension
Laws of Motion
Work, Energy and Power
Laws of Motion
- Aristotle’s Fallacy
- The Law of Inertia
- Newton's First Law of Motion
- Newton’s Second Law of Motion
- Newton's Third Law of Motion
- Conservation of Momentum
- Equilibrium of a Particle
- Common Forces in Mechanics
- Circular Motion and Its Characteristics
- Solving Problems in Mechanics
- Static and Kinetic Friction
- Laws of Friction
- Inertia
- Intuitive Concept of Force
- Dynamics of Uniform Circular Motion - Centripetal Force
- Examples of Circular Motion (Vehicle on a Level Circular Road, Vehicle on a Banked Road)
- Lubrication - (Laws of Motion)
- Law of Conservation of Linear Momentum and Its Applications
- Rolling Friction
- Introduction of Motion in One Dimension
Work, Energy and Power
- Introduction of Work, Energy and Power
- Notions of Work and Kinetic Energy: the Work-energy Theorem
- Kinetic Energy (K)
- Work Done by a Constant Force and a Variable Force
- Concept of Work
- Potential Energy (U)
- Conservation of Mechanical Energy
- Potential Energy of a Spring
- Various Forms of Energy : the Law of Conservation of Energy
- Power
- Collisions
- Non - Conservative Forces - Motion in a Vertical Circle
Motion of System of Particles and Rigid Body
System of Particles and Rotational Motion
- Motion - Rigid Body
- Centre of Mass
- Motion of Centre of Mass
- Linear Momentum of a System of Particles
- Vector Product of Two Vectors
- Angular Velocity and Its Relation with Linear Velocity
- Torque and Angular Momentum
- Equilibrium of Rigid Body
- Moment of Inertia
- Theorems of Perpendicular and Parallel Axes
- Kinematics of Rotational Motion About a Fixed Axis
- Dynamics of Rotational Motion About a Fixed Axis
- Angular Momentum in Case of Rotation About a Fixed Axis
- Rolling Motion
- Momentum Conservation and Centre of Mass Motion
- Centre of Mass of a Rigid Body
- Centre of Mass of a Uniform Rod
- Rigid Body Rotation
- Equations of Rotational Motion
- Comparison of Linear and Rotational Motions
- Values of Moments of Inertia for Simple Geometrical Objects (No Derivation)
Gravitation
Gravitation
- Kepler’s Laws
- Newton’s Universal Law of Gravitation
- The Gravitational Constant
- Acceleration Due to Gravity of the Earth
- Acceleration Due to Gravity Below and Above the Earth's Surface
- Acceleration Due to Gravity and Its Variation with Altitude and Depth
- Gravitational Potential Energy
- Escape Speed
- Earth Satellites
- Energy of an Orbiting Satellite
- Geostationary and Polar Satellites
- Weightlessness
- Escape Velocity
- Orbital Velocity of a Satellite
Properties of Bulk Matter
Mechanical Properties of Solids
- Elastic Behaviour of Solid
- Stress and Strain
- Hooke’s Law
- Stress-strain Curve
- Young’s Modulus
- Determination of Young’s Modulus of the Material of a Wire
- Shear Modulus or Modulus of Rigidity
- Bulk Modulus
- Application of Elastic Behaviour of Materials
- Elastic Energy
- Poisson’s Ratio
Thermodynamics
Behaviour of Perfect Gases and Kinetic Theory of Gases
Mechanical Properties of Fluids
- Thrust and Pressure
- Pascal’s Law
- Variation of Pressure with Depth
- Atmospheric Pressure and Gauge Pressure
- Hydraulic Machines
- Streamline and Turbulent Flow
- Applications of Bernoulli’s Equation
- Viscous Force or Viscosity
- Reynold's Number
- Surface Tension
- Effect of Gravity on Fluid Pressure
- Terminal Velocity
- Critical Velocity
- Excess of Pressure Across a Curved Surface
- Introduction of Mechanical Properties of Fluids
- Archimedes' Principle
- Stoke's Law
- Equation of Continuity
- Torricelli's Law
Oscillations and Waves
Thermal Properties of Matter
- Heat and Temperature
- Measurement of Temperature
- Ideal-gas Equation and Absolute Temperature
- Thermal Expansion
- Specific Heat Capacity
- Calorimetry
- Change of State - Latent Heat Capacity
- Conduction
- Convection
- Radiation
- Newton’s Law of Cooling
- Qualitative Ideas of Black Body Radiation
- Wien's Displacement Law
- Stefan's Law
- Anomalous Expansion of Water
- Liquids and Gases
- Thermal Expansion of Solids
- Green House Effect
Thermodynamics
- Thermal Equilibrium
- Zeroth Law of Thermodynamics
- Heat, Internal Energy and Work
- First Law of Thermodynamics
- Specific Heat Capacity
- Thermodynamic State Variables and Equation of State
- Thermodynamic Process
- Heat Engine
- Refrigerators and Heat Pumps
- Second Law of Thermodynamics
- Reversible and Irreversible Processes
- Carnot Engine
Kinetic Theory
- Molecular Nature of Matter
- Gases and Its Characteristics
- Equation of State of a Perfect Gas
- Work Done in Compressing a Gas
- Introduction of Kinetic Theory of an Ideal Gas
- Interpretation of Temperature in Kinetic Theory
- Law of Equipartition of Energy
- Specific Heat Capacities - Gases
- Mean Free Path
- Kinetic Theory of Gases - Concept of Pressure
- Assumptions of Kinetic Theory of Gases
- RMS Speed of Gas Molecules
- Degrees of Freedom
- Avogadro's Number
Oscillations
- Periodic and Oscillatory Motion
- Simple Harmonic Motion (S.H.M.)
- Simple Harmonic Motion and Uniform Circular Motion
- Velocity and Acceleration in Simple Harmonic Motion
- Force Law for Simple Harmonic Motion
- Energy in Simple Harmonic Motion
- Some Systems Executing Simple Harmonic Motion
- Damped Simple Harmonic Motion
- Forced Oscillations and Resonance
- Displacement as a Function of Time
- Periodic Functions
- Oscillations - Frequency
- Simple Pendulum
Waves
- Reflection of Transverse and Longitudinal Waves
- Displacement Relation for a Progressive Wave
- The Speed of a Travelling Wave
- Principle of Superposition of Waves
- Introduction of Reflection of Waves
- Standing Waves and Normal Modes
- Beats
- Doppler Effect
- Wave Motion
- Speed of Wave Motion
- Conservation of mechanical energy
- Principle of conservation of Energy
- Conservative forces
- Non-conservative forces
Notes
Conservative & Non-Conservative Forces
-
Conservative forces are those for which work done depends only on initial and final points.
Example- Gravitational force, Electrostatic force. -
Non-Conservative forces are those where the work done or the kinetic energy did depend on other factors such as the velocity or the particular path taken by the object.
Example- Frictional force.
The Conservation of Mechanical Energy
For conservative forces the sum of kinetic and potential energies of any object remains constant throughout the motion.
According to the quantum physics, mass and energy are not conserved separately but are conserved as a single entity called ‘mass-energy’.
-
Mechanical Energy is the energy associated with the motion and position of an object.
-
The quantity K +V(x), is called the total mechanical energy of the system.
-
For a conservative force, ΔK = ΔW = F(x) Δx
Also, - V(x) = F(x) Δx -
This employs Δ(K+V) =0 for a conservative force.
-
Individually the kinetic energy K and the potential energy V(x) may vary from point to point, but the sum is a constant.
Conservative Force:
-
A force F(x) is conservative if it can be derived from a scalar quantity V(x) by the relation : F(x) = - dv/dx
-
The work done by the conservative force depends only on the end points.
-
A third definition states that the work done by this force in a closed path is zero.
-
The total mechanical energy of a system is conserved if the forces, doing work on it, are conservative.
The above discussion can be made more concrete by considering the example of the gravitational force once again and that of the spring force in the next section. Fig. below depicts a ball of mass m being dropped from a cliff of height H.
The total mechanical energies E0, Eh, and EH of the ball at the indicated heights zero (ground level), h and H, are
`E_H = mgH`
`E_h = mgh + 1/2 mv_h^2`
`E_0 = (1/2) mv_f^2`
The constant force is a special case of a spatially dependent force F(x). Hence, the mechanical energy is conserved. Thus
`E_H = E_0`
`mgH = 1/2 mv_f^2`
`v_f= sqrt(2gH)`
a result for a freely falling body.
Further,
`E_H=E_h`
which implies,
`v_h^2 = 2g (H-h)`
and is a familiar result from kinematics.
At the height H, the energy is purely potential. It is partially converted to kinetic at height h and is fully kinetic at ground level. This illustrates the conservation of mechanical energy.
