}]]}]}]}] 30:T69e5,

### Physical World & Measurement - **Science & Physics:** - **Science:** Systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. - **Physics:** The natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. - **Physical Quantities:** - **Fundamental Quantities:** Independent quantities that cannot be expressed in terms of other physical quantities (e.g., Length, Mass, Time). - **Derived Quantities:** Quantities that can be expressed in terms of fundamental quantities (e.g., Velocity, Force, Energy). - **Units of Measurement:** - **SI Units (International System of Units):** - Length: meter (m) - Mass: kilogram (kg) - Time: second (s) - Electric Current: Ampere (A) - Temperature: Kelvin (K) - Luminous Intensity: Candela (cd) - Amount of Substance: Mole (mol) - **Supplementary Units:** Radian (rad) for plane angle, Steradian (sr) for solid angle. - **Dimensions and Dimensional Analysis:** - **Dimension:** The nature of a physical quantity (e.g., Length [L], Mass [M], Time [T]). - **Dimensional Formula:** An expression showing how and which fundamental units are involved in a physical quantity (e.g., Velocity $[LT^{-1}]$, Force $[MLT^{-2}]$). - **Principle of Homogeneity of Dimensions:** Only quantities of the same dimensions can be added, subtracted, or equated. Useful for checking formula correctness and deriving relationships. - **Measurement Errors:** - **Absolute Error ($\Delta x$):** The magnitude of the difference between the true value and the measured value. - **Relative Error:** $\frac{\text{Absolute Error}}{\text{True Value or Mean Value}}$ - **Percentage Error:** Relative Error $\times 100\%$ - **Types of Errors:** - **Systematic Errors:** Errors due to faulty instruments, imperfect experimental techniques, or personal bias. Can be minimized. - **Random Errors:** Errors due to unpredictable fluctuations in experimental conditions or personal judgment. Cannot be eliminated but can be minimized by taking many readings. - **Gross Errors:** Errors due to carelessness of the observer. - **Significant Figures:** Digits in a measurement that carry meaning contributing to its precision. Rules for counting and operations. ### Vectors - **Scalar vs. Vector Quantities:** - **Scalar:** Has only magnitude (e.g., mass, speed, time, distance, temperature). - **Vector:** Has both magnitude and direction (e.g., displacement, velocity, acceleration, force, momentum). - **Representation of Vectors:** Geometrically by directed line segments (arrows), analytically by components. - **Types of Vectors:** - **Unit Vector ($\hat{A}$):** A vector with magnitude 1, used to specify direction. $\hat{A} = \frac{\vec{A}}{|\vec{A}|}$. - **Null Vector (Zero Vector):** A vector with zero magnitude and arbitrary direction. - **Equal Vectors:** Two vectors are equal if they have the same magnitude and direction. - **Negative Vector:** A vector with the same magnitude but opposite direction. - **Collinear Vectors:** Vectors acting along the same line (parallel or anti-parallel). - **Coplanar Vectors:** Vectors lying in the same plane. - **Position Vector ($\vec{r}$):** A vector from the origin to a point. - **Vector Addition:** - **Triangle Law:** If two vectors are represented by two sides of a triangle taken in order, their resultant is represented by the third side taken in opposite order. - **Parallelogr