Physics Study Notes - Introduction to Classical Physics I

Lecture Overview

• Course: PHYS-2310 - Introduction to Classical Physics I

• Instructor: Prof. Raquel A. Ribeiro

• Institution: Iowa State University

Key Concepts

• Potential energy

• Kinetic energy

• Normal force

• Friction

Outline of Topics

• Scientific Notation

• Dimensional Analysis

• Vectors - part I

Scientific Notation

• Definition: A method to express very large or very small numbers using powers of 10.

• General Form: N imes 10^n

• Examples:

  • 3,000,000 = 3 imes 10^6

  • 0.00042 = 4.2 imes 10^{-4}

Dimensional Analysis

• Definition: A technique used to verify the consistency of physical equations through dimensions.

• Base Dimensions:

  • [M] = Mass

  • [L] = Length

  • [T] = Time

• Examples:

  • Velocity: Velocity = rac{Distance}{Time} yields dimensions [L][T^{-1}]

  • Force: Force = Mass imes Acceleration yields dimensions [M][L][T^{-2}]

Exercise: Dimensional Consistency

• Equation: F = Mv^2r + x d^3 t

• Required Dimensions: For components r and x to maintain dimensional consistency.

• Where:

  • F = Force

  • v = Velocity

  • M = Mass

  • d = Distance

  • t = Time

Solution Part 1

• Analyze the equation:

• F = kg rac{m}{s^2} for Force

• M = kg for Mass

• v = rac{m}{s} for Velocity

• d = m for Distance

• t = s for Time

Solution Part 2

• Dimensions of r:

  • r must have the dimension of distance, thus r = m.

• Revised Equation: F = Mv^2r + xd^3t

Solution Part 3

• Dimensions of x:

  • x must have the dimension of rac{Mass imes Distance^2}{Time^3}.

• Conclusion: x = kg rac{m^2}{s^3}

Fundamental Quantities

• Calculated from Fundamental Quantities:

  • Derived quantities can be expressed as combinations of fundamental quantities.

  • Examples include:

  • Area: m^2, derived from Length imes Length

  • Density: rac{kg}{m^3}, derived from Mass / (Length imes Length imes Length)

  • Velocity: rac{m}{s}, derived from Length / Time

  • Acceleration: rac{m}{s^2}, derived from Length / (Time imes Time)

  • Force: N (Newton) = rac{kg imes m}{s^2}, derived from rac{Mass imes Length}{(Second imes Second)}

  • Energy: J (Joule) = rac{kg imes m^2}{s^2}, derived from rac{Mass imes Length^2}{(Second imes Second)}

Dimensional Analysis - Unit Conversion

• Unit Conversion Example 1:

  • Convert 1 year to seconds:

  • 1 ext{ year} = 365.25 imes 24 imes 60 imes 60 ext{ seconds} = 31,557,600 ext{ s}

• Unit Conversion Example 2:

  • Convert 1 cubic meter to cubic centimeters:

  • 1 ext{ m} = 100 ext{ cm}

  • Therefore, 1 ext{ m}^3 = (100 ext{ cm})^3 = 1.0 imes 10^6 ext{ cm}^3

• Unit Conversion Example 3:

  • Convert 1 foot-pound to Joules:

  • 1 ext{ ft} = 0.30484 ext{ m}

  • 1 ext{ ft-pound}
    ightarrow 1.35582 ext{ J}

Geometric Figures - 2D Shapes

• Square:

  • Perimeter: P = 4s

  • Area: A = s^2

• Rectangle:

  • Perimeter: P = 2L + 2W

  • Area: A = LW

• Parallelogram:

  • Perimeter: P = 2L + 2W

  • Area: A = Lh

• Rhombus:

  • Area: A = rac{1}{2} pq

• Triangle:

  • Perimeter: P = a + b + c

  • Area: A = rac{1}{2} bh

• Circle:

  • Perimeter (Circumference): P = 2 ext{π}R

  • Area: A = ext{π}R^2

Geometric Figures - 3D Shapes

• Cube:

  • Surface Area: SA = 6s^2

  • Volume: V = s^3

• Rectangular Prism:

  • Surface Area: SA = 2(lw + lh + wh)

  • Volume: V = lwh

• Cylinder:

  • Surface Area: SA = 2B + 2 ext{π}rh

  • Volume: V = Bh

• Sphere:

  • Surface Area: SA = 4 ext{π}r^2

  • Volume: V = rac{4}{3} ext{π}r^3

Right Triangle Trigonometric Functions

• Definitions:

  • ext{sin} heta = rac{b}{c}

  • ext{cos} heta = rac{a}{c}

  • ext{tan} heta = rac{b}{a}

• Pythagorean Theorem:

  • c^2 = a^2 + b^2

Scalars

• Definition: A scalar is a quantity characterized solely by magnitude, with no direction.

• Examples: Mass, temperature, energy, charge.

• Operations: Scalar addition, subtraction, multiplication, and division follow conventional algebra.

Vectors

• Definition: A vector is a quantity that possesses both magnitude and direction; often represented as an