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## Physics 101 Notes: Chapter 1 ### Measurements * Physics is based on **measurement**. * We need units to describe these measurements. #### SI Units * Also known as the metric system * Time: Seconds (s) * Length: Meter (m) * Mass: Kilogram (kg) #### Other Systems of Units * Brit...

## Physics 101 Notes: Chapter 1 ### Measurements * Physics is based on **measurement**. * We need units to describe these measurements. #### SI Units * Also known as the metric system * Time: Seconds (s) * Length: Meter (m) * Mass: Kilogram (kg) #### Other Systems of Units * British System (still used in the US) * cgs (centimeter, gram, second) #### Derived Units * Units like $m/s$ for speed are derived from the fundamental units. * Area is measured in $m^2$, Volume in $m^3$ ### Unit Conversions * We can convert units * Example: 1 inch = 2.54 cm * 5 inches = $5 \text{ inches} \times \frac{2.54 \text{ cm}}{1 \text{ inch}} = 12.7 \text{ cm}$ ### Order of Magnitude * Physicists often make approximations * We are often interested in getting within a factor of 10 * How tall is your instructor? * Closest: 2m * Could be 1m, could be 3m, but probably not 10m ### Dimensional Analysis * Dimensions are not the same as units. * Dimensions of length, mass, and time are $[L]$, $[M]$, and $[T]$ * We can check equations using dimensional analysis. * Area = Length x Length $\rightarrow [L^2]$ * Volume = Length x Length x Length $\rightarrow [L^3]$ ### Trigonometry #### Degrees vs. Radians * Full circle = $360^\circ = 2\pi$ radians * $1 \text{ radian} = \frac{360}{2\pi} \approx 57.3^\circ$ #### Trig Functions * $\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$ * $\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$ * $\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$ #### Common Values | Degrees | Radians | $\sin(\theta)$ | $\cos(\theta)$ | $\tan(\theta)$ | | :------ | :-------------- | :------------- | :------------- | :------------- | | 0 | 0 | 0 | 1 | 0 | | 30 | $\frac{\pi}{6}$ | $\frac{1}{2}$ | $\frac{\sqrt{3}}{2}$| $\frac{1}{\sqrt{3}}$ | | 45 | $\frac{\pi}{4}$ | $\frac{\sqrt{2}}{2}$| $\frac{\sqrt{2}}{2}$ | 1 | | 60 | $\frac{\pi}{3}$ | $\frac{\sqrt{3}}{2}$ | $\frac{1}{2}$ | $\sqrt{3}$ | | 90 | $\frac{\pi}{2}$ | 1 | 0 | $\infty$ | ### Vectors * Vectors have a magnitude and a direction. * Examples: velocity, force #### Adding Vectors * Tip-to-tail method * Place the tail of the second vector at the tip of the first vector. * The resultant vector goes from the tail of the first to the tip of the second. #### Components of Vectors * $A_x = A\cos(\theta)$ * $A_y = A\sin(\theta)$ * $A = \sqrt{A_x^2 + A_y^2}$ * $\theta = \tan^{-1}(\frac{A_y}{A_x})$ ### Coordinate Systems * We can choose different coordinate systems, but physics does not depend on the choice. * Usually we use Cartesian coordinates (x, y, z) or Polar coordinates (r, $\theta$).