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 → Motion ↓


Circular motion


Circular motion is a fascinating concept in physics that explains the motion of objects on a circular path. It is an important part of mechanics, and understanding it can help us understand how things around us move. In this article, we will explore various aspects of circular motion and provide examples and formulas to help explain the concepts in a clear and simple way.

What is circular motion?

Circular motion refers to the motion of an object along the circumference of a circle or moving along a circular path. The study of circular motion involves understanding the forces and angles that cause objects to move in this unique way.

Circular motion can be uniform or non-uniform. In uniform circular motion, the speed of the object is constant, however its velocity is not constant as the direction changes continuously. In non-uniform circular motion, both speed and velocity change.

Examples of circular motion

There are many examples of circular motion in our daily lives. Let's take a look at a few:

  • Revolving door: When you push a revolving door to enter a building, the door spins in a circular path around a central point.
  • Ferris wheel: As it spins, each of its cabins rotates in a circular path around the central axis.
  • Earth's orbit around the Sun: A classic example of circular motion in space where the Earth moves in a nearly circular orbit around the Sun.
  • Merry-Go-Round: When it moves around in parks, it has a circular motion.

Let's visualize circular motion with an illustration:

object radius (r)

Understanding velocity and acceleration in circular motion

While studying circular motion, it is necessary to understand the concept of velocity and acceleration:

Velocity

In circular motion the velocity is tangential, which means that at any given point, the direction of the velocity vector is tangential to the circle. In uniform circular motion the magnitude of this velocity remains constant, and it changes direction as the object moves.

Acceleration

Even in uniform circular motion, there is always an acceleration towards the centre of the circle. This is called centripetal acceleration. It only changes the direction of the velocity, not the magnitude.

The formula for centripetal acceleration is:

a = v 2 / r

Where:

  • a is the centripetal acceleration,
  • v is the speed,
  • r is the radius of the circle.

Visual representation of velocity and acceleration in circular motion:

V A

Centripetal force

Centripetal force is the force that keeps an object moving in a circular path. It acts toward the center of the circle and is necessary for any kind of circular motion.

The formula for centripetal force is given as:

F = m * v 2 / r

Where:

  • F is the centripetal force,
  • m is the mass of the object,
  • v is the speed of the object,
  • r is the radius of the circle.

Example of centripetal force

Suppose a car is moving at a speed of 20 m per second on a circular path of radius 50 m. If the mass of the car is 1000 kg, what is the centripetal force acting on the car?

F = m * v 2 / r = 1000 * (20) 2 / 50 = 8000 N

The centripetal force acting on the car is 8000 Newton.

Types of circular motion

Uniform circular motion

In uniform circular motion, the object moves along a circular path at a constant speed. While the speed remains constant, the direction of motion constantly changes, causing a change in velocity. This type of motion is common in objects orbiting planets and satellites.

Non-uniform circular motion

Non-uniform circular motion occurs when the speed of the object varies as it moves along a path. This is seen in a merry-go-round which speeds up or slows down as it spins.

Mathematical representation of circular motion

Angular velocity

Angular velocity is a measure of how quickly an object rotates around its center. It is represented by the Greek letter omega (ω). Angular velocity is related to the speed of the object and the radius of the circle by the formula:

ω = v / r

Where:

  • ω is the angular velocity,
  • v is the linear velocity,
  • r is the radius.

Duration and frequency

The period (T) is the time taken to make one complete revolution around the circle, while the frequency (f) is the number of revolutions per unit time. They are related by the formula:

f = 1 / T

Example: If a wheel rotates 3 times per second, its frequency is 3 Hz, and its period is 1/3 second.

Applying the concept of circular motion

Practical applications

The principles of circular motion are applied in a variety of real-world scenarios:

  • Roller Coasters: Engineers use the concept of circular motion to design safe and thrilling rides.
  • Astronomy: To understand how planets orbit stars and how moons orbit planets, we need to use the rules of circular motion.
  • Vehicle Tyres: The rotation of vehicle tyres is a simple example of circular motion.

Problem solving with circular motion

Solving problems involving circular motion often involves determining unknown variables using the formulas for centripetal force, velocity, and period. Here's an example problem:

Example problem: A cyclist is cycling at a speed of 6 meters per second on a circular path with a radius of 10 meters. If the cyclist's mass is 70 kg, calculate the centripetal acceleration and the centripetal force.

a = v 2 / r = 6 2 / 10 = 3.6 m/s 2

The centripetal acceleration is 3.6 m / s 2.

F = m * a = 70 * 3.6 = 252 N

The centripetal force is 252 Newtons.

Understanding these principles helps us understand how force and motion combine to create the various motions we see.

Conclusion

Circular motion is an important aspect of physics that helps us understand the motion of various objects in our universe. From the simple rotation of a door to the complex orbit of planets, circular motion governs how things move in a circle. By understanding the basics of centripetal force, velocity, acceleration, and angular velocity, students gain insight into the laws that govern circular paths. Mastering these concepts leads to a deeper understanding of the universe and the fundamental laws of motion.


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Circular motion

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