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


Dynamics is a branch of physics that deals with the study of forces and their effects on the motion of objects. Unlike kinematics, which deals only with the description of motion, dynamical physics explains why objects move. Understanding dynamics is important for explaining the motion of everything from tiny particles to galaxies. At its core, dynamics is based on Newton's laws of motion.

Newton's laws of motion

As an introductory text, Newton's laws of motion form the basis for dynamics. They explain how forces affect motion:

  1. Newton's First Law: Often called the law of inertia, it states that an object at rest remains at rest and an object in motion continues to move with the same speed and in the same direction unless an unbalanced force is applied.
  2. Newton's Second Law: The acceleration of an object is proportional to the net force applied to it and inversely proportional to its mass. This is usually formulated as F = ma, where F is the applied force, m is the mass of the object, and a is the acceleration.
  3. Newton's Third Law: For every action there is an equal and opposite reaction. This means that forces always come in pairs; if object A exerts a force on object B, then object B exerts an equal but opposite force on object A.

Understanding the force

Force is a vector quantity, which means it has both magnitude and direction. Common forces in physics include gravitational force, tension, friction, and normal force. Here, we will discuss these in simple terms.

Gravitational force

Gravitational force is the force of attraction between two masses. On Earth, it gives weight to physical objects and makes them fall to the ground, such as when an apple is plucked from a tree. The force can be calculated using the formula:

F = G * (m1 * m2) / r^2

Where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between the centers of the two masses.

Tension

Tension is the force operating along the length of a wire or string when it is pulled by forces acting from the opposite end. It is used in cases involving ropes, cables, and wires. If you pull a rope to lift a box, the tension of the rope supports the box against gravity.

Force Tension Mass

Friction

Friction is the force that opposes the motion of an object. It acts parallel to the surface with which the object is in contact. For example, when you slide a book across a table, friction acts against the motion. The general formula for friction force is:

f = μ * N

Here, f is the friction force, μ is the coefficient of friction (a measure of how rough the contact surfaces are), and N is the normal force (the perpendicular force applied to the object).

Friction Surface

Normal force

Normal force is the supporting force applied to an object that is in contact with another stationary object. It is perpendicular to the contact surface. For example, a book placed on a table is acted upon by an upward normal force, which counteracts its weight.

Normal force

Applications of dynamics

Dynamics is used in many real-world scenarios, from engineering to sports. Let's look at some examples where understanding dynamics is important.

Vehicles

Engines provide the thrust (force) to move the car, the wheels grip the road due to friction, and aerodynamics determine how efficiently the vehicle moves through the air. Engineers use dynamics to design vehicles that are safe, fast, and fuel-efficient.

When a car accelerates, it follows Newton's second law, where the total force is determined by the power of the engine (transformed into thrust) and the friction between the tires and the road.

Sports

Athletes use dynamics in sports. For example, throwing a basketball involves understanding how much force is needed to get the ball into the hoop. The correct amount of force, angle, and spin is calculated consciously or unconsciously using the principles of dynamics.

Astronomy

In astronomy, dynamics helps us understand the behavior of celestial bodies. The motion of planets, stars, and galaxies is governed by gravitational forces. Newton's law of gravitation helps explain the orbits of planets and the motion of galaxies.

Problem solving with dynamics

Dynamics involves a systematic approach to solving problems. Here's a simple guide:

  1. Identify all forces acting on the body. Draw a free-body diagram if necessary.
  2. Write the equations of motion using Newton's laws.
  3. Solve equations for unknown values such as force, acceleration, or velocity.

Example problem

Suppose you have a block of mass 5 kg on a frictionless surface, which is being pulled to the right by a force of 20 N. What is the acceleration of the block?

Using Newton's second law: F = ma

We rearrange the formula to solve for the acceleration a:

a = F / m

Substitute the following values:

a = 20 N / 5 kg = 4 m/s²

Thus, the acceleration of the block is 4 m/s².

Simplifying force

When analyzing forces, it is often helpful to break them down into components. For example, when dealing with an inclined plane, forces can be divided into perpendicular and parallel components. This helps simplify complex dynamics problems.

MG Perpendicular Parallel

Conclusion

Dynamics is a fundamental aspect of physics that explains how forces cause changes in motion. Its principles are applied in many areas, from designing systems that ensure the safety of structures to understanding cosmic movements. Mastering dynamics begins with understanding Newton's laws and understanding forces, leading to great problem-solving skills that can be employed in many disciplines. Continue exploring examples of real-world dynamics, solve various physics problems, and make connections between theoretical principles and practical applications. This knowledge is a vital part of our understanding of the physical world.


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Dynamics

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