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


Mechanics is the branch of physics that deals with the motion of objects and the forces that affect motion. It helps us understand how and why objects move and allows us to predict future motion given initial conditions. Mechanics is a foundational concept in physics, drawing on ideas from mathematics and physics such as velocity, acceleration, force, and energy to describe motion.

Types of mechanics

Mechanics can be broadly divided into two categories:

  • Dynamics: The branch that studies motion without considering its causes. It includes parameters like displacement, velocity and acceleration.
  • Kinematics: Unlike dynamics, dynamics deals with the forces and torques that affect motion.

Dynamics

Kinematics describes motion using specific terms:

  • Displacement: It is a vector quantity that represents the change in position of an object. If an object moves from point A to B, then the straight line distance between A and B is displacement.
  • Velocity: It is the rate of change of displacement. It is also a vector quantity. Velocity can be expressed by the formula: v = Δx / Δt
  • Speed: Unlike velocity, speed is a scalar quantity that measures total distance traveled over time.
  • Acceleration: It is the rate of change of velocity over time. If the speed is increasing, the object is accelerating. If the speed is decreasing, it is called deceleration or negative acceleration. The formula is: a = Δv / Δt

Visual example

        <svg width="400" height="110"> <rect x="10" y="10" width="30" height="30" style="fill:blue;" /> <text x="50" y="35" fill="black">→ movement >→ Displacement</text> </svg>
        <svg width="400" height="110"> <rect x="10" y="10" width="30" height="30" style="fill:blue;" /> <text x="50" y="35" fill="black">→ movement >→ Displacement</text> </svg>

While kinematics considers only how objects move, dynamics considers the causes of motion:

Newton's laws of motion

An essential part of dynamics is Newton's laws of motion, which are as follows:

  1. First Law (Law of Inertia): An object at rest remains at rest, and an object in motion continues to move at a constant velocity unless an external force is applied on it. This law highlights the concept of inertia, which is the tendency of an object to resist a change in its state of motion. For example, a book kept on a table will remain at rest unless a force is applied to move it.
  2. Second Law (Law of Acceleration): The acceleration of an object is proportional to the net force applied on the object and inversely proportional to the mass of the object. It can be mathematically formulated as: F = m * a where 'F' is force, 'm' is mass, and 'a' is acceleration.
  3. Third Law (Action and Reaction): For every action there is an equal and opposite reaction. This means that forces always come in pairs. For example, when you push a wall, the wall also pushes with an equal force.

Visual example

        <svg width="400" height="180"> <line x1="50" y1="80" x2="350" y2="80" style="stroke:rgb(99,99,99);stroke-width:2"></line> <circle cx="70" cy="80" r="20" style="fill:lime;stroke:purple;stroke-width:2" /> <line x1="70" y1="60" x2="70" y2="0" style="fill:none;stroke:red;stroke-width:2" /> <text x="80" y="30" fill="red"><- Force</text> </svg>
        <svg width="400" height="180"> <line x1="50" y1="80" x2="350" y2="80" style="stroke:rgb(99,99,99);stroke-width:2"></line> <circle cx="70" cy="80" r="20" style="fill:lime;stroke:purple;stroke-width:2" /> <line x1="70" y1="60" x2="70" y2="0" style="fill:none;stroke:red;stroke-width:2" /> <text x="80" y="30" fill="red"><- Force</text> </svg>

Work, energy and power

Energy is an important concept in dynamics, and is closely related to work and power:

Work

Work is done when a force applied to an object causes displacement. The formula for work is: Work = force x displacement x cos(θ) Here, θ is the angle between the direction of the force and the direction of displacement.

Energy

Energy is the capacity to do work and it can take several forms:

  • Kinetic energy: The energy of an object due to its motion. It is expressed as: KE = 1/2 m v² where 'm' is mass and 'v' is velocity.
  • Potential energy: Energy stored due to an object's position or state. For example, gravitational potential energy is: PE = m * g * h where 'm' is mass, 'g' is acceleration due to gravity, and 'h' is height.

Power

Power is the rate at which work is done or energy is transferred. The formula is: Power = work / time

Conservation laws

There are a number of conservation laws in mechanics, such as:

Energy conservation

This law states that the total energy in a closed system remains constant over time. Energy can neither be created nor destroyed; it only changes form. For example, when a ball is dropped, its gravitational potential energy is converted into kinetic energy.

Conservation of momentum

The total momentum of a closed system remains constant unless an external force acts on it. Momentum is the product of mass and velocity: p = m * v

Visual example: Energy conversion

        <svg width="200" height="200"> <line x1="50" y1="100" x2="150" y2="100" stroke="blue" stroke-width="4" /> <text x="80" y="80" fill="black">Potential Energy</text> <text x="80" y="120" fill="black">Kinetic Energy</text> <text x="80" y="140" fill="green">Total Energy remains constant</text> </svg>
        <svg width="200" height="200"> <line x1="50" y1="100" x2="150" y2="100" stroke="blue" stroke-width="4" /> <text x="80" y="80" fill="black">Potential Energy</text> <text x="80" y="120" fill="black">Kinetic Energy</text> <text x="80" y="140" fill="green">Total Energy remains constant</text> </svg>

Applications of mechanics

Mechanics is not just theoretical; it has many real-world applications, including:

  • Engineering: Understanding forces and motion is essential to design structures and machinery.
  • Astronomy: Mechanics helps explain the motion of celestial bodies.
  • Everyday life: From driving a car to playing sports, mechanics plays a vital role in understanding motion.

Conclusion

Understanding mechanics introduces fundamental concepts that inform the broader study of physics. From the motion of cars on the road to planets in space, mechanics helps us understand and map physical motion.


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