Lecture Notes: Dynamics and Motion Principles

Introduction

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• Video covers syllabus outlines.

Linear Momentum

• Definition: Product of mass (m) and velocity (v).
  • Formula: ( p = mv )
  • Units: kg m/s or Newton Second
• Characteristics:
  • Vector quantity, direction same as velocity.

Newton’s Laws of Motion

• First Law (Law of Inertia):
  • A body remains at rest or in uniform motion unless acted on by a force.
  • Mass measures inertia.
• Second Law:
  • Resultant force equals the rate of change of momentum.
  • ( F = \frac{\Delta p}{t} ) or ( F = ma )
  • Impulse: Change in momentum, with units same as momentum.
• Third Law:
  • For every action, there is an equal and opposite reaction.
  • Equal magnitude, opposite direction, act on different bodies.

Collisions and Impulse

• Example: Ball hitting a wall
  • Change in momentum calculation involving negative sign for direction.
  • Forces during collision obey Newton’s Third Law.
• Graphical Understanding:
  • Momentum-time graph: Gradient represents force.

Worked Examples

• Example 1: Tension in a string with a moving pebble
  • Upward and downward motion calculations using ( F = ma ).
• Example 2: System with masses on a pulley
  • Acceleration and tension calculations.
  • Force on a pulley and kinematic equations for distance.
• Example 3: Box and friction problem
  • Acceleration calculation with frictional force.

Additional Concepts

• Conservation of Momentum:
  • Total momentum before and after collision is equal.
  • Applies to closed systems with no external forces.
• Momentum in Explosions:
  • Momentum conservation applies to fragments after explosion.
• Types of Collisions:
  • Elastic: Conservation of both momentum and kinetic energy.
  • Inelastic: Conservation of momentum but not kinetic energy.

Exam Style Questions

• Examples provided to apply principles:
  • Calculating tension, acceleration, and forces.
  • Applying conservation laws in collisions and explosions.

Friction and Drag Forces

• Friction: Opposes motion, converts kinetic energy to thermal energy.
• Drag: Friction in a fluid, affected by surface area and speed.
• Terminal Velocity: Velocity when forces are balanced.
  • Graphical analysis of velocity, displacement, and acceleration.

Application Examples

• Skydiver’s changing acceleration due to drag.
• Golf ball rebounding, changes in momentum.

Mass and Weight

• Mass: Scalar, constant in the universe, unit kg.
• Weight: Vector, depends on gravitational field strength, unit Newtons.

Closing Notes

• Emphasis on the value of understanding dynamics and motion for problem-solving.
• Encourage engagement for future content.