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 → Gravitational force → Universal gravitation ↓


Newton's law of universal gravitation


Introduction

Newton's law of universal gravitation is a fundamental principle that describes how objects in the universe attract each other with a force called gravity. This concept is important in understanding the behavior of celestial bodies and terrestrial phenomena. In simple terms, this law states that every mass attracts every other mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Interpretation of the law

The mathematical expression of Newton's law of universal gravitation is given as follows:

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

Where:

  • F is the gravitational force between the two masses.
  • G is the gravitational constant, which is approximately equal to 6.674 × 10^-11 N(m/kg)^2.
  • m1 and m2 are the masses of the two objects.
  • r is the distance between the centers of the two masses.

Visualization of gravitational attraction

Let's imagine this gravitational attraction between two objects:

M1 M2 F R item 1 Item 2

Importance of the gravitational constant

The gravitational constant G is important for calculating the gravitational force between two masses. Its small value indicates that the gravitational force is relatively weak compared to other fundamental forces, such as the electromagnetic force. Despite its weakness, gravity has significant effects over long distances and is the dominant force governing the motion of celestial bodies such as planets, stars and galaxies.

In-universe examples

The following examples show the application of Newton's law of universal gravitation:

Example: Earth and Moon

The gravitational attraction between the Earth and the Moon keeps the Moon in orbit around the Earth. If the mass of the Earth is m1 = 5.972 × 10^24 kg and the mass of the Moon is m2 = 7.348 × 10^22 kg, and the average distance r = 384,400 km, we can calculate the gravitational force:

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

Substituting the values:

F = 6.674 × 10^-11 * (5.972 × 10^24 * 7.348 × 10^22) / (384,400,000^2)

After calculation, the force is about 1.98 × 10^20 N

Example: Apple and Earth

Why does an apple fall from a tree? Consider the Earth, which has a mass of 5.972 × 10^24 kg, and an apple, which has a mass of 0.1 kg, that is about 1 m above the ground. We can calculate the force of gravity using:

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

Plugging in the values:

F = 6.674 × 10^-11 * (5.972 × 10^24 * 0.1) / 1^2

After calculation, the force is about 0.98 N, which is the force pulling the apple towards the earth.

Inverse square law

1 / r^2 term in the formula refers to the inverse square law. This means that the gravitational force decreases with the square of the distance between the objects. If you double the distance between two objects, the gravitational force becomes one-fourth as strong. This principle is important when calculating gravitational forces over astronomical distances.

Implications of the law

Newton's law of universal gravitation has several important implications:

  • It explains why planets revolve around stars and why moons revolve around planets.
  • It describes the tides on Earth caused by the gravitational forces of the Moon and the Sun.
  • It provides the basis for understanding more complex theories such as general relativity.

Conclusion

Newton's law of universal gravitation is a cornerstone of physics, providing information about the force that governs the motion of celestial bodies and objects on Earth. Understanding this law helps unravel the mysteries of the universe, from the orbits of planets to the behavior of galaxies.

By recognizing the relationship between mass and distance in gravitational attraction, we gain a deeper understanding of the delicate balance and order in the universe. This fundamental concept not only explains past observations but also guides future explorations of the universe.


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Newton's law of universal gravitation

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