Concept Card: Frame of Reference, Distance & Displacement in 1D Motion 1. Frame of Reference: A frame of reference is a coordinate system (Cartesian axes $x, y, z$) attached to an observer along with a calibrated clock to record the time coordinate $t$. Inertial Frame of Reference: A frame in which Newton’s First Law of … Read more
Concept Card: Master Review & Strategy Sheet for Units, Errors & Dimensions 1. Dimensional Analysis Master Relations: The dimensions of any physical quantity $Q$ are represented as $[Q] = [M^a L^b T^c A^d K^e \text{mol}^f \text{cd}^g]$. Fundamental Electromagnetic Dimensionless Ratios: Fine-structure constant: $\alpha = \frac{e^2}{4\pi \varepsilon_0 \hbar c} \approx \frac{1}{137} \implies [M^0 L^0 T^0]$ Speed … Read more
Concept Card: Applications & Limitations of Dimensional Analysis 1. The Principle of Homogeneity of Dimensions: The Principle of Homogeneity states that a physical equation is dimensionally valid if and only if every term on both sides of the equation has the exact same dimensional formula. If an equation has the general form: $A = B […]
Concept Card: Dimensions of Physical Quantities & Dimensional Formulae 1. Definition of Dimensions: The dimensions of a physical quantity are the powers (or exponents) to which the fundamental base quantities must be raised to represent that quantity. The standard dimensional expression is represented in terms of the seven base dimensions: $[Q] = [M^a L^b T^c … Read more
Concept Card: Errors in Measurement & Propagation of Errors 1. Classification of Experimental Errors: Error is the difference between the true value and the measured value of a physical quantity: Systematic Errors: Errors that tend to occur consistently in one direction (either consistently positive or consistently negative). Instrumental errors: Imperfect calibration or zero error of […]
Concept Card: Least Count of Measuring Instruments & Significant Figures 1. Least Count (LC) of Measuring Instruments: The least count is the smallest value that can be directly measured by an instrument. It defines the precision and instrumental resolution limit. A. Vernier Calipers: $\text{Least Count (LC)} = 1\text{ Main Scale Division (MSD)} – 1\text{ Vernier […]
Concept Card: Systems of Units & Physical Quantities 1. Physical Quantities & Invariance: A physical quantity $Q$ is completely expressed by a numerical value $n$ and a unit $u$: $Q = n \times u$ Since the physical magnitude remains constant regardless of the measurement scale: $n_1 u_1 = n_2 u_2 = \text{constant} \implies n \propto … Read more
Work Done by a Constant Force & Dot Product Worksheet This is a worksheet based on lecture “Work Done by Constant Force and Dot Product“ Level 1 Practice Worksheet Questions Q1. The SI unit of work done is equivalent to: (a) $\text{kg}\cdot\text{m/s}$ (b) $\text{kg}\cdot\text{m}^2/\text{s}^2$ (c) $\text{kg}\cdot\text{m}/\text{s}^2$ (d) $\text{kg}\cdot\text{m}^2/\text{s}^3$ Q2. The dimensional formula for work done … Read more
Summary This is Lecture 12 (last lecture) for the topic “Work, Energy and Power”. You can find all resources related with Work, Energy and Power by clicking on this link. Here we will cover the concept of Elastic collision and inelastic collisions in Two Dimensions and different aspects of it. 1. Introduction to Oblique Collisions When two bodies … Read more
Summary This is Lecture 11 for the topic “Work, Energy and Power”. You can find all resources related with Work, Energy and Power by clicking on this link. Here we will cover the concept of Inelastic Collisions in one dimension, coefficient of restitution and different aspects of it. 1. Introduction to Inelastic Collisions In the real world, nearly … Read more