Classical Mechanics Overview

Classical Mechanics

• Definition: The branch of physics dealing with the motion of objects and the forces acting upon them.

• Key Laws:

  • Newton's Laws of Motion:
    1. First Law (Inertia): An object at rest stays at rest, and an object in motion stays in motion unless acted upon by a net force.
    2. Second Law (F=ma): The acceleration (a) of an object is directly proportional to the net force (F) acting on it and inversely proportional to its mass (m).
    3. Third Law: For every action, there is an equal and opposite reaction.

• Kinematics:

  • Studies motion without considering forces.
  • Key equations relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).
    • ( v = u + at )
    • ( s = ut + \frac{1}{2} at^2 )
    • ( v^2 = u^2 + 2as )

• Dynamics:

  • Focuses on the effects of forces on motion.
  • Includes concepts such as:
    • Force: A push or pull on an object (measured in Newtons).
    • Weight: The gravitational force acting on an object, calculated as ( W = mg ).

• Work and Energy:

  • Work (W): Done when a force causes displacement; ( W = F \cdot d \cdot \cos(\theta) ).
  • Kinetic Energy (KE): Energy of motion, given by ( KE = \frac{1}{2} mv^2 ).
  • Potential Energy (PE): Energy stored due to position, commonly gravitational ( PE = mgh ).
  • Conservation of Energy: Total mechanical energy (KE + PE) remains constant in absence of non-conservative forces.

• Momentum:

  • Defined as ( p = mv ).
  • Conservation of Momentum: In a closed system, momentum before an event equals momentum after the event.

• Rotational Motion:

  • Describes the motion of objects that rotate about an axis.
  • Key concepts:
    • Angular Displacement: The angle through which an object rotates.
    • Torque (τ): The rotational equivalent of linear force, ( τ = rF \sin(\theta) ).
    • Moment of Inertia (I): A measure of an object's resistance to change in its rotation.

• Gravitation:

  • Described by Newton's Law of Universal Gravitation: ( F = G \frac{m_1 m_2}{r^2} ).
  • Objects attract each other with a force that depends on their masses and the distance between them.

• Oscillations and Waves:

  • Study of periodic motion (e.g., pendulums, springs).
  • Key parameters include amplitude, frequency, period, and phase.

• Applications:

  • Engineering (design of structures and machines).
  • Astrophysics (motion of celestial bodies).
  • Everyday phenomena (transportation, sports).

Classical Mechanics

• Classical mechanics is a branch of physics that studies the motion of objects and the forces acting on them.

• Newton's Laws of Motion are fundamental:

  • First Law: An object at rest remains at rest, and an object in motion continues in motion at a constant velocity unless acted upon by a net force.
  • Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This is represented by the equation F = ma, where F is force, m is mass, and a is acceleration.
  • Third Law: For every action, there is an equal and opposite reaction.

Kinematics

• Kinematics is the study of motion without considering the forces that cause it.
• Key equations relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t):
  • ( v = u + at )
  • ( s = ut + \frac{1}{2} at^2 )
  • ( v^2 = u^2 + 2as )

Dynamics

• Dynamics focuses on the effects of forces on motion.
• Force: A push or pull on an object, measured in Newtons.
• Weight: The gravitational force acting on an object, calculated as ( W = mg ), where m is mass and g is the acceleration due to gravity.

Work and Energy

• Work (W) is done when a force causes displacement, calculated as ( W = F \cdot d \cdot \cos(\theta) ), where F is force, d is displacement, and θ is the angle between the force and displacement.
• Kinetic Energy (KE) is the energy of motion, given by ( KE = \frac{1}{2} mv^2 ).
• Potential Energy (PE) is the energy stored due to position. A common example is gravitational potential energy, which is calculated as ( PE = mgh ), where m is mass, g is acceleration due to gravity, and h is height.
• Conservation of Energy: The total mechanical energy (KE + PE) remains constant in the absence of non-conservative forces.

Momentum

• Momentum (p) is defined as ( p = mv ), where m is mass and v is velocity.
• Conservation of Momentum: In a closed system, the total momentum before an event equals the total momentum after the event.

Rotational Motion

• Rotational motion describes the motion of objects that rotate around an axis.
• Angular Displacement: The angle through which an object rotates.
• Torque (τ): The rotational equivalent of linear force, ( τ = rF \sin(\theta) ), where r is the distance from the axis of rotation to the point where the force is applied, F is the force, and θ is the angle between the force and the lever arm.
• Moment of Inertia (I): A measure of an object's resistance to change in its rotation. It depends on the mass distribution of the object.

Gravitation

• Newton's Law of Universal Gravitation states that ( F = G \frac{m_1 m_2}{r^2} ), where F is the force of gravity, G is the gravitational constant, ( m_1 ) and ( m_2 ) are the masses of the two objects, and r is the distance between their centers.
• This law describes the attraction between any two objects with mass.

Oscillations and Waves

• Oscillations and waves are the study of periodic motion.
• Key parameters include:
  • Amplitude: The maximum displacement from equilibrium.
  • Frequency: The number of oscillations per unit time.
  • Period: The time for one complete oscillation.
  • Phase: The position of an oscillating object at a particular time.

Applications of Classical Mechanics

• Classical mechanics is essential in many fields, including:
  • Engineering: Designing structures and machines.
  • Astrophysics: Studying the motion of celestial bodies.
  • Everyday phenomena: Understanding transportation, sports, and other aspects of our daily lives.

Introduction to Light

• Light is a form of energy traveling at 3.8 x 10^8 meters per second (speed of light) through space and into our atmosphere.
• Light is a form of electromagnetic radiation.
• Light is made up of wave patterns consisting of both electric and magnetic fields.

Anatomy of Electromagnetic Waves

• Wavelength: Measured in nanometers (nm), represents the distance between two peaks or troughs of a wave.
• Frequency: Measured in Hertz (Hz), represents the number of waves passing a point per second.

Inverse Relationship Between Wavelength and Frequency

• Wavelength and frequency are inversely proportional.
• Longer wavelengths correspond to lower frequencies and lower energy radiation.
• Shorter wavelengths correspond to higher frequencies and higher energy radiation.

Electromagnetic Spectrum

• The electromagnetic spectrum arranges radiation from low to high energy.
• Visible light is the only portion of the electromagnetic spectrum that humans can see.
• Visible light, also known as white light, is comprised of seven colors: red, orange, yellow, green, blue, indigo, and violet.
• Visible light occupies a minuscule portion of the electromagnetic spectrum, highlighting its small scale compared to other forms of electromagnetic waves.

History of the Electromagnetic Spectrum

• Isaac Newton was the first to study color.
• He passed sunlight through a prism, separating it into different colors.
• This demonstrated that visible light consists of red, orange, yellow, green, blue, indigo, and violet.
• Each color corresponds to specific wavelengths and frequencies.
• Newton's experiment explains the phenomenon of rainbows, where sunlight is split into colors by water droplets.

Animals and Different Wavelengths

• Some animals see wavelengths invisible to humans.
• Bees can see ultraviolet light, while goldfish can see infrared light.
• These abilities are adaptations that aid survival in specific environments and result from evolutionary processes.

Sources of Light

• Natural sources: Emit their own light, such as the Sun.
• Artificial sources: Emit light due to external energy input, like a light bulb or candle.

Light Production

• We see objects because light enters our eyes from them.
• The Sun emits its own light, while other objects reflect it.
• Luminous objects: Produce their own light (e.g., the Sun, a light bulb, a lit match).
• Non-luminous objects: Reflect light from other sources (e.g., trees, textbooks, pencils).

Ray Model of Light

• Light travels in straight lines.
• Light ray: A line representing the direction and path of light travel on a diagram.
• Geometric optics: Uses light rays to determine the path of light when it interacts with objects.

Clarity of Objects

• Transparent: Allows light to pass through easily (e.g., glass).
• Translucent: Allows some light to pass through (e.g., frosted glass).
• Opaque: Blocks all light from passing through (e.g., a wall).

Mirrors

• A mirror is any surface that reflects light.
• Reflection: The bouncing back of light from a surface.
• Image: A reproduction of an object created by reflected light.
• We see reflected images because some light rays bounce off the surface and travel into our eyes.

Important Definitions for Mirror Diagrams

• Plane mirror: A flat mirror that helps illustrate predictable paths of light.
• Incident ray: The incoming light ray from a source.
• Reflected ray: The light ray that bounces off the mirror.
• Normal: A line perpendicular to the mirror's surface.
• Slash lines: Indicate the back or non-reflective surface of a mirror.

Mirror Diagrams

• Arrows indicate the direction of light ray travel.
• Dashed lines represent the backside of the mirror.
• ∠i = angle of incidence, ∠r = angle of reflection.

Laws of Reflection

• Angle of incidence = angle of reflection: ∠i = ∠r.
• The incident ray, reflected ray, and normal all lie within the same plane.

Reflecting Light Off Surfaces

• Specular reflection: Occurs when light reflects off a smooth surface, resulting in a clear reflection (e.g., a mirror).
• Diffuse reflection: Occurs when light reflects off a rough surface, producing scattered reflections (e.g., a wall).