Physics

Measurements and Uncertainty in Physics (IB)

Key Concepts

1. Measurement

  • Definition: The process of obtaining the magnitude of a quantity relative to a standard unit.

  • Units: Standardized quantities (e.g., meter, kilogram, second) used for measurement.

2. Types of Measurements

  • Direct Measurement: Obtaining a value directly using instruments (e.g., ruler, thermometer).

  • Indirect Measurement: Calculating a value based on other measurements (e.g., using formulas).

3. Significant Figures

  • Definition: Digits in a number that contribute to its precision.

  • Rules:

    • Non-zero digits are always significant.

    • Any zeros between significant digits are significant.

    • Leading zeros are not significant.

    • Trailing zeros in a decimal number are significant.

4. Uncertainty

  • Definition: An estimate of the amount by which a measured or calculated value could differ from the true value.

  • Types:

    • Absolute Uncertainty: The uncertainty of a measurement expressed as a fixed quantity (e.g., ±0.1 m).

    • Relative Uncertainty: The uncertainty expressed as a fraction or percentage of the measurement (e.g., ±0.1 m / 2 m = 5%).

5. Sources of Uncertainty

  • Instrumental Uncertainty: Limitations of measuring devices (e.g., resolution).

  • Human Error: Mistakes made by the observer (e.g., parallax error).

  • Environmental Factors: External conditions affecting measurements (e.g., temperature, pressure).

6. Propagation of Uncertainty

  • Addition/Subtraction: Combine absolute uncertainties.

    • Total Uncertainty = √(u₁² + u₂² + ... + uₙ²)

  • Multiplication/Division: Combine relative uncertainties.

    • Total Relative Uncertainty = √((u₁/a₁)² + (u₂/a₂)² + ... + (uₙ/aₙ)²)

7. Reporting Results

  • Format: Results should be reported with the appropriate number of significant figures and include uncertainty.

  • Example: ( 5.67 \pm 0.02 , \text{m} )

8. Graphical Representatio

Mind Map: Mechanics in IBHL Physics

Central Idea

Mechanics

Main Branches

1. Kinematics

  • Displacement

    • Definition

    • Vector vs. Scalar

  • Velocity

    • Average Velocity

    • Instantaneous Velocity

  • Acceleration

    • Uniform Acceleration

    • Non-Uniform Acceleration

  • Equations of Motion

    • SUVAT equations

    • Graphical representation

2. Dynamics

  • Newton's Laws of Motion

    • First Law (Inertia)

    • Second Law (F=ma)

    • Third Law (Action-Reaction)

  • Forces

    • Types of Forces (Contact, Non-contact)

    • Friction

    • Tension

    • Normal Force

  • Free Body Diagrams

    • Drawing Techniques

    • Analyzing Forces

3. Energy

  • Work

    • Definition

    • Work-Energy Principle

  • Kinetic Energy

    • Formula

    • Conservation of Energy

  • Potential Energy

    • Gravitational Potential Energy

    • Elastic Potential Energy

  • Power

    • Definition

    • Calculating Power

4. Momentum

  • Linear Momentum

    • Definition

    • Conservation of Momentum

  • Impulse

    • Relationship to Momentum

    • Calculating Impulse

  • Collisions

    • Elastic vs. Inelastic Collisions

    • Conservation Laws

5. Circular Motion

  • Uniform Circular Motion

    • Centripetal Force

    • Centripetal Acceleration

  • Angular Motion

    • Angular Displacement

    • Angular Velocity

    • Angular Acceleration

  • Torque

    • Definition

    • Calculation

6. Oscillations

  • Simple Harmonic Motion (SHM)

    • Characteristics

    • Equations of SHM

  • Energy in SHM

    • Kinetic and Potential Energy

  • Damping and Resonance

    • Types of Damping

    • Resonance Phenomena

7. Gravitation

  • Newton's Law of Gravitation

    • Gravitational Force

    • Gravitational Field Strength

  • Orbits

    • Kepler's Laws

    • Satellites and Gravity

  • Kinematics: Displacement: Vector quantity representing change in position

    Kinematics: Velocity: Rate of change of displacement; vector quantity

    Kinematics: Acceleration: Rate of change of velocity; vector quantity

    Newton's Laws: First Law: An object remains at rest or in uniform motion unless acted upon by a net force

    Newton's Laws: Second Law: F = ma; force equals mass times acceleration

    Newton's Laws: Third Law: For every action, there is an equal and opposite reaction

    Work-Energy Principle: Work done on an object equals the change in its kinetic energy

    Conservation of Energy: Total energy in a closed system remains constant

    Momentum: Product of mass and velocity; conserved in isolated systems

    Circular Motion: Acceleration directed towards the center; centripetal force required