1.1 Measurements in Physics
Fundamental Units
| Quantity | SI Unit | Symbol |
|---|---|---|
| Lenght | meter | m |
| Mass | kilogram | kg |
| Time | second | s |
| Current | ampere | A |
| Temperature | Kelvin | K |
| Amount of Substance | mole | mol |
| Luminous intensity | candela | cd |
Rules for significant digits
1.Every non zero digit is significant
2.Zeros between two significant digits are significant
3.Zeros to the right of a significant digit and a decimal point are significant
Metric multipliers (Prefixes)
| Factor | Name | Symbol |
|---|---|---|
| 1015 | Peta | P |
| 1012 | Tera | T |
| 109 | Giga | G |
| 106 | Mega | M |
| 103 | Kilo | k |
| 102 | Hecto | h |
| 101 | Deca | da |
| 10-3 | milli | m |
| 10-6 | micro | µ |
| 10-9 | nano | n |
| 10-12 | pico | p |
Metric conversion
1. Simple conversion (fundamental unit to a prefix)
\begin{equation*} \left(\frac{given\ value\ \ given\ unit}{1}\right)\left(\frac{desired\ unit}{undesired\ unit}\right) \end{equation*}Example: 590.1g -> ng
\begin{equation} \left(\frac{590.1g}{1}\right)\left(\frac{1ng}{10^{-9} g}\right) =590.1*10^{9} ng \end{equation}2. Double conversion (prefix to a prefix)
\begin{equation} \left(\frac{given\ value\ \ given\ unit}{1}\right)\left(\frac{desired\ unit}{undesired\ unit}\right)\left(\frac{desired\ prefix}{undesired\ prefix}\right) \end{equation}Example: 706.0 Mm -> nm
\begin{equation} \left(\frac{706.0Mm}{1}\right)\left(\frac{10^{6} m}{1Mm}\right)\left(\frac{1nm}{10^{-9} m}\right) =7.060*10^{17} nm \end{equation}3. Complex conversion (trick - denominator)
\begin{equation} {\textstyle \left(\frac{given\ value\ \ given\ unit}{1}\right)\left(\frac{desired\ unit}{undesired\ unit}\right)\left(\frac{desired\ prefix}{undesired\ prefix}\right)\left(\frac{undesired\ time}{desired\ time}\right)} \end{equation}Example: 0.00705µg/s -> dag/hr
\begin{equation} {\textstyle \left(\frac{0.00705µ g}{1}\right)\left(\frac{10^{-6} g}{1µ g}\right)\left(\frac{1dag}{10^{1} g}\right)\left(\frac{3600s}{h}\right)} \end{equation}Accuracy and precision
Precision in experiments
Precision for analog instruments: half the least increment
Precision for digital instruments: to the last measured digit
1.2 Uncertainties and errors
\begin{gather*}
absolute\ uncertainty\ =\ \Delta x\\
fractional\ uncertainty\ =\ \frac{\Delta x}{x}\\
percentage\ uncertainty\ =\ \frac{\Delta x}{x} \ *\ 100\%
\end{gather*}
\begin{gather*}
y=a\pm b,\ \Delta y=\Delta a+\Delta b\\
y=\frac{a*b}{c} ,\ \frac{\Delta y}{y} =\frac{\Delta a}{a} +\frac{\Delta b}{b} +\frac{\Delta c}{c}\\
y=a^{n} ,\ \frac{\Delta y}{y} =\frac{n\Delta a}{a}
\end{gather*}
Random and systematic errors
| Random Error | Systematic Error |
|---|---|
| -Fluctuations in measurements centered around the true value -Reduced by taking the average -Affects precision Examples: -Human error -Inconsistent room temperature |
-Fixed shift in measurement away from the true value -Affects accuracy Examples: -Zero offset error -Bad method of measurement -Incorrect callibration |
3 Ways of calculating uncertainty of processed data
(1) Range method(2) Use the equations
(3) Percentage uncertainty
Uncertainties in graphs
-Linear best fit line: max and min lines-Non-linear best fit line: linearization
-Error bars: horizontal or vertical, lenght of two absolute uncertainties
-Types of graphs
1.3 Vectors and Scalars
Vectors and scalars
| Vector | Scalar |
|---|---|
| -Magnitude and Direction Examples: -Acceleration -Force -Displacement -Velocity |
-Magnitude Examples: -Time -Energy -Speed -Distance |
Vector operations
(1) Scalar operation
\begin{gather*}
\vec{A} =\ 4.00\ cm\\
3\vec{A} \ =\ 12.00\ cm\\
\frac{1}{2}\vec{A} \ =\ 2.00\ cm
\end{gather*}
(2) Addition and subtraction
(3) Dot product
\begin{equation*}
a\cdot b=\parallel a\parallel \parallel b\parallel cosθ
\end{equation*}
(4) Cross product
\begin{equation*}
a\times b=\begin{vmatrix}
i & j & k\\
a_{1} & a_{2} & a_{3}\\
b_{1} & b_{2} & b_{3}
\end{vmatrix}
\end{equation*}
Resolving vectors
Topic 1 Problems
Number of correct answers: