Mastering Physics

Mastering Physics

 Chapter 1 - Introduction to Physics

Highlighting System

Summary

• Goal in physics is to gain understanding of the universe
• Everything in nature obeys the laws of physics 
• Physics can help us learn the ‘why’ and ‘how’ in nature 
• The basic laws and principles are the focus 

• Issues to consider (important to learning physics)

• System of measurement (mass, length, time)
• Numerical calculations
• Mathematical notations
• Goal thru these issues is to create language in which will help you with your understanding in physics

Recap

Goal is to understand and question the universe around you using language you will learn through being taught physics

(1-1) Physics and the Laws of Nature 

Physics - the study of integral laws of nature; laws that are the reason for physical phenomena in the universe

• Laws can be expressed thru math
• Precise science, deeply rooted in theory and experiment

(1-2) Units of Length, Mass, Time 

• Why do we need to measure basic physical quantities?

• In order to make quantitative (precise) comparisons

• Quantities:

• Length (L)
• Mass (M)
• Time (T)

• Begin with defining the units of measurement

• Ex. meters (length)

• SI units/mks units - meters (m), kilograms (kg), seconds (s)

Length

• Meter created as one 10 millionth of the distance between the Equator and the North Pole 

Typical Distance Measurement Table 

Mass

• Mass is measured in kilograms (kg) 
• Mass is intrinsic, unchanging while weight is the measure of gravity (g) acting on an object 
• Weight can vary on location of object 

• Ex. Your weight on Mars is diff. than on Earth 

Time 

• Time is measured based off the earth’s orbit
• Atomic clocks most accurate; based on frequencies of radiation emitted from certain atoms
• Atomic clock used for defining seconds with cesium-133 atoms (amount of time it takes for a cesium-133 atom to complete 9,192,631,770 cycles of oscillation)
• Oscillation - the process of moving back and forth; to swing between different states
• Frequency determined by cesium fountain atomic clock 

• Produces fountain of cesium atoms, vacuumed upwards to about a meter and take 1 second to rise and fall

(1-3) Dimensional Analysis

• Dimension - referring to the type of quantity

• Ex. distance measured in cubits and another distance measured in light-years are both referring to the same dimension (length)

• Velocity - the measure of the speed of something going in a certain direction 
• Velocity is measured by (length/time) ex. miles per hour
• Formulas in physics must be dimensionally consistent (each term in the equation must have the same dimensions) 
• Use brackets to mark dimensions in a quantity or equation

• Ex. r = radius, m = miles,   [r] = L     [m] = L  

(L = Length)

• Ex. v = velocity   v = [L]/[T]  (Length/Time)

• Dimension check good for looking over work

(1-4) Significant Figures

• Inaccuracy/uncertainty caused by instruments wrongly measuring quantities or by the senses of those carrying out the experiment
• Significant figs. - precise numbers when measuring quantities (ex. 3.4 seconds)
• The # of significant figs. after multiplying or dividing = the # least accurately known quantity
• When phys. quantities are added/subtracted: the # of decimal places after addition or subtraction is = to the smallest # of decimal places in any of the individual terms 

• Ex. rather than 2.14 - 1.05 being 1.09, it’s rounded to 1.1

• Conclusion: best to round up when necessary 

Scientific Notation 

• Zeros in significant figures count as significant figs. (including after decimal points)
• 2500 x 102m → there are 4 sig. figs. 

Round-off Error

• Round-off error - numbers being rounded off randomly during calculation, producing a slightly inaccurate #
• Keep extra number in digits
• Round off in final results to prevent inaccuracy 

(1-5) Converting Units

• When converting units, previous (unwanted) units will cancel out to result in expressing the quantity with transferred unit 

• Ex.   316 ft → meters      1m = 3.281 ft    

(316 ft)  (1m/3.281 ft) = 96.3 m

• In each conversion factor the numerator is the same as the denominator (ex. 1m = 3.281 ft, (1m/3.281 ft)) 

(1-6) Order-of-Magnitude Calculations 

• Order-of-magnitude calculation - rough estimate meant to be accurate within a factor of 10
• Gives one an idea of what’s to be expected from a complete (more precise) calculation
• Works in theory, especially when a precise number is too big to reach 

(1-7) Scalars and Vectors

• Quantities can be defined by only a #, or a # and a direction

• Ex. 25 m/s due north → velocity (rate of travel + direction)

• Scalars - quantities only specified by #
• Vector - quantity with both a # value and a direction 
• Direction of a velocity vector can only be up, down, right, left, etc. 

• Notation: A car going one way would be expressed mathematically as [(v1 = +25 m/s) → + is going in a positive direction]. 
• Another way would be [(v2 = -25 m/s) → - is going in the opposite/negative direction of car 1].
• Notation specifically for one-dimensional vectors

(1-8) Problem Solving in Physics

• Learn physics by interacting with physics
• Physics is CREATIVE

Guideline for Problem-Solving in Physics

• Read problem carefully

• Understand what info is given and what is being asked of you
• Pay attention to detail

• Sketch the system
• Visualize the physical process

• Use sketch to put system in motion

• Strategize

• Helps identify forces and variables in the process
• Ask what principles/concepts are at play
• Develop a strategy (your own process) to gain a definitive answer

• Identify appropriate equations

• Find equations that apply to the problem
• Important element in strat

• Solve the equation
• Check answer

• See if it makes sense (logically)
• Does it have the correct dimensions?
• Are the numbers reasonable? 

• Explore limits/special cases 

• Explore possibilities and alternatives to certain variables (what happens then?)