Grade 9
  1. Mechanics  1.1. Motion  1.1.1. Types of motion  1.1.2. Distance and displacement  1.1.3. Speed and Velocity  1.1.4. Acceleration  1.1.5. Graphical representation of motion  1.1.6. Equations of motion  1.1.7. Uniform and non-uniform motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Relative speed  1.1.10. Circular motion  1.2. Laws of force and motion  1.2.1. The concept of force  1.2.2. newton's first law of motion  1.2.3. Newton's second law of motion  1.2.4. Newton's third law of motion  1.2.5. Inertia and types of inertia  1.2.6. Motion  1.2.7. Conservation of momentum  1.2.8. Application of Newton's laws in daily life  1.2.9. Types of Forces (Contact and Non-Contact)  1.2.10. Friction and its effects  1.3. Gravitational force  1.3.1. Newton's law of universal gravitation  1.3.2. Importance of Gravitational Force  1.3.3. Acceleration due to gravity  1.3.4. Free fall and weightlessness  1.3.5. Mass and weight  1.3.6. Variation of g with height and depth  1.3.7. Kepler's laws of planetary motion  1.3.8. Satellites and their orbits  1.4. Work, Energy and Power  1.4.1. Concept of work  1.4.2. Positive and negative actions  1.4.3. Work done by constant and variable force  1.4.4. Energy and its forms  1.4.5. Kinetic energy and potential energy  1.4.6. Law of conservation of energy  1.4.8. Commercial unit of energy  1.4.9. Work–energy theorem  1.5. Simple machines  1.5.1. Types of simple machines  1.5.2. Mechanical advantage  1.5.3. Machine efficiency  1.5.4. Levers and their types  1.5.5. Pulleys and Inclined Planes  1.5.6. Gears and their uses
  2. Properties of matter  2.1. States of matter  2.1.1. Solids, liquids and gases  2.1.2. Properties of different states of matter  2.1.3. Change in state of matter  2.1.4. Plasma and Bose–Einstein condensate  2.2. Density and pressure  2.2.1. Concept of density and relative density  2.2.2. Pressure in solids, liquids and gases  2.2.3. Pascal's law and its applications  2.2.4. Atmospheric pressure and its variations  2.2.5. Surface tension and capillarity  2.3. Buoyancy and Archimedes' principle  2.3.1. Buoyant force  2.3.2. Archimedes principle  2.3.3. Applications of Archimedes' Principle  2.3.4. floating and sinking objects  2.3.5. Theory of Flotation and Archimedes' Principle
  3. Heat and Thermodynamics  3.1. Temperature and heat  3.1.1. Concept of heat and temperature  3.1.2. Temperature measurement  3.1.3. Temperature scales  3.2. Heat transfer  3.2.1. Conduction of heat  3.2.2. Convection of heat  3.2.3. heat radiation  3.2.4. Applications of heat transfer  3.2.5. Thermal conductivity  3.3. Thermal expansion  3.3.1. Expansion of solids, liquids and gases  3.3.2. Abnormal expansion of water  3.3.3. Applications of Thermal Expansion  3.4. Specific heat capacity and latent heat  3.4.1. Concept of specific heat capacity  3.4.2. Measurement and applications of specific heat  3.4.3. Latent heat of fusion and vaporization  3.4.4. Heat Engines and Efficiency
  4. Waves and sound  4.1. Waves and their types  4.1.1. Mechanical and electromagnetic waves  4.1.2. Longitudinal and Transverse Waves  4.1.3. Properties of Waves  4.1.4. Wavelength, frequency and speed of the wave  4.1.5. Superimposition of waves  4.2. Sound waves  4.2.1. Nature and transmission of sound  4.2.2. Speed of sound in different mediums  4.2.3. Reflection of sound and echo  4.2.4. Sonar and ultrasound  4.2.5. Resonance and pulsation  4.3. Sound characteristics  4.3.1. Intensity, loudness and quality of sound  4.3.2. Doppler effect in sound
  5. Lighting and Optics  5.1. Reflection of light  5.1.1. Laws of reflection  5.1.2. Reflection from a plane mirror  5.1.3. Reflection from a spherical mirror  5.1.4. Image formation by concave and convex mirrors  5.1.5. Applications of Reflection  5.2. Refraction of light  5.2.1. Laws of refraction  5.2.2. Refractive index  5.2.3. Refraction through a glass slab  5.2.4. Refraction in water and air  5.2.5. Lenses and their types  5.2.6. Image formation by convex and concave lenses  5.2.7. Total internal reflection and its applications  5.3. Dispersion and scattering of light  5.3.1. Spectrum of white light  5.3.2. Prisms and Dispersion  5.3.3. Tyndall effect and blue sky
  6. Electricity and Magnetism  6.1. Electric charge and static electricity  6.1.1. The concept of electric charge  6.1.2. Charging by friction, contact and induction  6.1.3. Electroscope and its working  6.2. Current Electricity  6.2.1. The concept of electric current  6.2.2. Ohm's Law and Resistance  6.2.3. Factors affecting resistance  6.2.4. Series and Parallel Circuits  6.2.5. Heating effect of electric current  6.2.6. Electric power and energy  6.3. Magnetism  6.3.1. Natural and artificial magnets  6.3.2. Properties of magnets  6.3.3. Earth's magnetism  6.3.4. Magnetic field and field lines  6.3.5. Electromagnets and their applications
  7. Modern Physics  7.1. structure of the atom  7.1.1. Atomic Structure and Subatomic Particles  7.1.2. Electrons, Protons, and Neutrons  7.1.3. Rutherford and Bohr model  7.2. Radioactivity  7.2.1. Types of radioactive emissions  7.2.2. Half-life and radioactive decay  7.2.3. Uses and Hazards of Radioactivity
  8. Space science and astronomy  8.1. The universe and its components  8.1.1. Stars and galaxies  8.1.2. Planets and Solar System  8.2. Satellites  8.2.1. Natural and artificial satellites  8.2.2. Use of satellites

Grade 9 → Mechanics → Laws of force and motion ↓


Conservation of momentum


The principle of conservation of momentum is a fundamental concept in physics, especially when we study mechanics. It is a guideline that helps us understand how objects behave when they interact with each other. Simply put, momentum is a measure of the motion of an object and is calculated as the product of an object's mass and velocity.

What is speed?

Before diving into the conservation aspect, let us first clarify what is meant by momentum. Momentum is a vector quantity, which means it has both magnitude and direction. The mathematical representation of momentum (p) can be given as:

p = m * v

Where m is the mass of the object and v is its velocity.

Understanding momentum with an example

Imagine a truck and a car, both moving down the highway at the same speed. The truck has more momentum because it has more mass than the car. Even though their velocities are the same, the truck's larger mass gives it more impact when it stops or changes its speed. This illustration shows that momentum depends on both the object's speed and mass.

Explanation of conservation of momentum

Now that we understand what momentum is, let's discuss the conservation of momentum. This principle states that if there is no external force acting on a system, then the total momentum of the system remains constant. It can be expressed in mathematical terms as follows:

p initial = p final

or if it contains more than one item:

m 1 * v 1i + m 2 * v 2i = m 1 * v 1f + m 2 * v 2f

Here, v 1i and v 2i are the initial velocities, and v 1f and v 2f are the final velocities of objects 1 and 2, respectively.

This theorem is true whether bodies collide or push each other and can be observed in various real-life scenarios.

An everyday example

Suppose you are standing on a skateboard and you throw a heavy ball in the forward direction. According to conservation of momentum, when you throw the ball, the skateboard moves in the opposite direction to balance the momentum of the thrown ball. This is because initially both you and the skateboard are at rest, so the total momentum is zero. When the ball is thrown, the skateboard moves to keep the total momentum zero.

Skateboard ball throw

In the above diagram, the ball is thrown in one direction, while the skateboard moves in the opposite direction to conserve momentum.

Applications of conservation of momentum

Conservation of momentum is not just a theoretical concept; it has many practical applications, from simple games such as pool or snooker to complex areas such as space travel.

In the game

In games like billiards or snooker, when the cue ball strikes another ball, the total momentum of the system (cue ball + object ball) before the collision is equal to the total momentum after the collision, provided there are no external forces like friction acting on them. This principle helps players to play accurate shots by estimating the speed of the ball after the strike.

In vehicles

This principle is important in understanding vehicle safety features, such as airbags. When cars crash, they stop suddenly, but the passengers inside continue moving at the same speed due to inertia. Airbags help reduce injuries by providing a cushioning force that changes the speed gradually.

In space missions

Spacecraft use conservation of momentum to travel through space. When a spacecraft needs to change its trajectory, it does so by venting gas, which causes the spacecraft to move in the opposite direction to preserve momentum.

Mathematics of conservation of momentum

To dig deeper, let's look at how the equations of motion work with conservation principles. Consider two objects with masses m 1 and m 2 moving with velocities v 1 and v 2 respectively before the collision. Their momenta are:

p 1 = m 1 * v 1
p 2 = m 2 * v 2

After collision, their velocities are v 1f and v 2f. The total initial momentum is:

p initial = m 1 * v 1 + m 2 * v 2

and the total final momentum is:

p final = m 1 * v 1f + m 2 * v 2f

Thus, according to the conservation principle:

m 1 * v 1 + m 2 * v 2 = m 1 * v 1f + m 2 * v 2f

Analyzing examples through equations

Let's consider a practical problem: Imagine two ice skaters pushing each other, each of whom has a different mass. Skater A, who has a mass of 50 kilograms, pushes skater B, who has a mass of 70 kilograms. If skater A moves at a speed of 3 meters per second after the push, and assuming they start from rest, how fast does skater B move?

Before the push, the total momentum was zero because both were stationary:

p initial = 0

The total momentum must be zero even after pushing away from each other, so:

m A * v A + m B * v B = 0

Substituting the known values:

50 kg * 3 m/s + 70 kg * v B = 0

Solving for v B:

v B = - (50 kg * 3 m/s) / 70 kg = -2.14 m/s

The negative sign indicates that Skater B moves in the opposite direction, which shows how they conserve momentum in the action.

Collision and motion

Collisions provide an ideal platform to study the conservation of momentum. There are two main types of collisions: elastic and inelastic. In elastic collisions, both momentum and kinetic energy are conserved, while in inelastic collisions, only momentum is conserved.

Elastic collision

Let us consider a situation where two perfectly elastic balls collide. Both momentum and kinetic energy remain unchanged before and after the collision. This type is often simplified and studied in controlled environments such as physics laboratories.

Inelastic collision

Most collisions in the real world are inelastic. Think of a car hitting an obstacle. Here, energy is transformed and not conserved as heat, sound, or deformation. However, momentum is still conserved, which is the beautiful simplicity of physics.

For example, when two cars collide and become entangled with each other, their final momentum as a single system will be equal to their initial total momentum before the collision.

Conclusion

Conservation of momentum provides an important framework for understanding a variety of phenomena that occur in physics and in our lives every day. Whether it is the collision of athletes on the playing field, vehicles on the highway, or navigating spacecraft in outer space, this principle provides clarity and consistency in predicting outcomes. Our explorations in physics are based on such essential principles, which fuel anticipation for further discoveries in various applications.


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Conservation of momentum

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