Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Mechanics ↓


dynamics


Kinematics is a branch of mechanics that deals with the motion of objects without considering the causes of their motion. In simple terms, it describes how things move, their speed, direction, and how these elements change over time. By understanding kinematics, we lay the groundwork for analyzing more complex motion scenarios in physics.

Basic concepts of dynamics

To study kinematics, we start with several key concepts: displacement, velocity, acceleration, and time.

Displacement

Displacement refers to the change in the position of an object. It is a vector quantity, meaning it has both magnitude and direction. Displacement is different from distance, which is a scalar quantity that shows how much ground and distance the object has traveled, regardless of direction.

Example: Imagine a straight road. If a car travels 50 m east from point A to point B, its displacement will be 50 m in the east direction, not just the distance of "50 m".

Displacement = 50 m east

Velocity

Velocity is a vector quantity that refers to the rate of change of displacement. It tells us how fast and in which direction an object is moving. Average velocity can be calculated using the formula:

Average Velocity = (Final Displacement - Initial Displacement) / Time Taken

Example: If the car travels from point A to point B in 5 seconds, then the average velocity is

Average Velocity = 50 meters East / 5 seconds = 10 meters per second East
Average velocity = 10 m/s east

Acceleration

Acceleration is the rate at which an object's velocity changes over time. Like velocity and displacement, acceleration is a vector quantity and can describe how an object speeds up, slows down, or changes direction.

The formula for acceleration is:

Acceleration = (Final Velocity - Initial Velocity) / Time Taken

Example: If the speed of a car increases from 10 m / s to 20 m / s in 5 s, then its acceleration will be:

Acceleration = (20 m/s - 10 m/s) / 5 seconds = 2 m/s^2

Equations of motion

There are three primary equations of motion that are used to describe the motion of objects assuming constant acceleration. These equations are helpful in solving a variety of problems in dynamics.

First equation of motion

The first equation relates velocity, acceleration and time. It is given as:

v = u + at

Where:

  • v is the final velocity
  • u is the initial velocity
  • a is the acceleration
  • It's time

This equation helps in finding the velocity of an object at any time, provided its initial velocity and constant acceleration are given.

Second equation of motion

The second equation connects displacement with initial velocity, time, and acceleration:

s = ut + (1/2)at^2

Where:

  • s is the displacement
  • u is the initial velocity
  • It's time
  • a is the acceleration

This equation allows us to calculate the displacement of an object under constant acceleration.

Third equation of motion

The third equation allows us to calculate the velocity, initial velocity, and displacement:

v^2 = u^2 + 2as

where the symbols represent the same quantities as mentioned before.

Example: These equations can be used in a variety of practical scenarios, such as estimating how far a car will travel before stopping or determining the take-off speed of an airplane based on the length of a certain runway.

Visual representation of motion

Imagine you are watching an object moving in a straight line. The motion can be represented descriptively through a graph:

Position-time graph

A position-time graph shows how the position of an object changes over time. The slope of the line on a position-time graph represents the velocity of the object.

Time Post slope = velocity

A straight line represents constant velocity, while a curved line represents changing velocity (acceleration).

Velocity-time graphs

Velocity-time graph shows how the velocity of an object changes with time. The slope of the velocity-time graph shows the acceleration of the object.

Time Velocity slope = acceleration

The area under the velocity-time graph represents the displacement of the object during a given period of time.

Projectile motion

Projectile motion is a type of kinematics problem in which an object is released into the air and moves under the influence of gravity. The motion can be divided into two components: horizontal and vertical.

The horizontal motion of a projectile is uniform because it has no acceleration (neglecting air resistance), while the vertical motion is uniformly accelerated due to gravity.

Horizontal Distance Vertical Height

The equations of motion can be applied separately to the horizontal and vertical components to solve for various aspects of the projectile's trajectory, such as maximum altitude, time of flight, and range.

Practical applications of dynamics

Understanding kinematics is important in many fields. Engineers apply these principles to design vehicles, amusement park rides, and safety systems. Athletes and coaches use kinematic principles to improve performance and reduce the risk of injury. Scientists rely on kinematics to model natural phenomena such as the orbits of planets or the flight paths of rockets.

Summary and conclusion

Kinematics provides a detailed analysis of the basic forms of motion. It provides the tools to describe the motion of objects in terms of displacement, velocity, and acceleration over time. The equations of motion simplify the relationships between these quantities under constant acceleration. Visual representations such as graphs provide further insight into the characteristics of motion. By mastering the fundamentals of kinematics, one gains the ability to understand and predict the behavior of moving objects in a wide range of practical scenarios.


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