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
Kinematics
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
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
Work, Energy and Power
- Introduction of Work, Energy and Power
- Notions of Work and Kinetic Energy: the Work-energy Theorem
- Kinetic Energy
- Work Done by a Constant Force and a Variable Force
- Concept of Work
- The Concept of Potential Energy
- 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 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
Motion of System of Particles and Rigid Body
Laws of Motion
Work, Energy and Power
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
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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)
Properties of Bulk Matter
Gravitation
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
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- Adiabatic Processes
Behaviour of Perfect Gases and Kinetic Theory of Gases
Mechanical Properties of Solids
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
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- 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
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
Waves
- Gravitational Potential Energy and Gravitational Potential
Notes
Gravitational Potential Energy
-
Potential energy is due to the virtue of position of the object.
-
Gravitational Potential Energy is due to the potential energy of a body arising out of the force of gravity.
-
Consider a particle which is at a point P above the surface of earth and when it falls on the surface of earth at position Q, the particle is changing its position because of force of gravity.
-
The change in potential energy from position P to Q is same as the work done by the gravity.
-
It depends on the height above the ground and mass of the body.
Expression for gravitational potential energy:
Case 1: 'g' is Constant.
Consider an object of mass 'm' at point A on the surface of the earth.
work done will be given as;
`"W"_("BA")="FX"` Displacement where F=gravitational force exerted towards the earth.
=mg(h2-h1) (body is brought from position A to B)
=mgh2 - mgh1
WAB = VA - VB
Where,
VA = potential energy at point A
VB = Potential energy at point B
From above equation we can say that the work done in moving the particle is just the difference of potential energy between its final and initial positions.
Case 2: 'g' is not constant.
Calculate work done in lifting a particle from r = r1 to r = r2(r2 > r1) along a vertical path .
we will get, W=V(r2) - V(r1)
Conclusion:
In general the gravitational potential energy at a distance 'r' is given by `"V"(r)=-("GM"_em)/"r" + "V"_o`
where,
V(r)= potential energy at a distance 'r'.
Vo = At this point gravitational potential energy is zero.
Gravitational potential energy is `prop` to the mass of the particle.
Problem:
Choose the correct alternative:
- Acceleration due to gravity increases/decreases with increasing altitude.
- Acceleration due to gravity increases/decreases with increasing depth. (assume the earth to be a sphere of uniform density).
- Acceleration due to gravity is independent of mass of the earth/mass of the body.
- The formula – `GMm(1/r_2– 1/r_1)` is more/less accurate than the formula `"mg"(r_2– r_1)` for the difference of potential energy between two points r2and r1 distance away from the centre of the earth.
Answer:
(a)Decreases
(b)Decreases
(c)Mass of the body
(d)More
Explanation:
Acceleration due to gravity at depth h is given by the relation:
`"gh" = (1- "2h"/R_E)g`
Where,
RE = Radius of the Earth, g = acceleration due to gravity on the surface of the earth.
It is clear from the given relation that acceleration due to gravity decreases with an increase in height.
Acceleration due to gravity at depth d is given by the relation:
`"gd"=(1-"d"/"R"_E)g`
It is clear from the given relation that acceleration due to gravity decreases with an increase in depth.
Acceleration due to gravity of body of mass m is given by the relation: `"g"="GM"/"r"^2`
Where,
G = Universal gravitational constant
M = Mass of the Earth
R = Radius of the Earth
Hence, it can be inferred that acceleration due to gravity is independent of the mass of the body.
Gravitational potential energy of two points r2 and r1 distance away from the centre of the Earth is respectively given by:
`"V"(r_1) = - "GmM"/r_1`
`"V"(r_2) = -"GmM"/r_2`
Therefore,
Difference in potential energy, V = V(r2) – V(r1) =-GmM (1/r2 – 1/r1)
Hence, this formula is more accurate than the formula mg (r2– r1).
