Concept Card: Newton’s Third Law of Motion & Action-Reaction Pairs 1. Formal Statement of Newton’s Third Law: To every action, there is always an equal and opposite reaction; or the mutual interactions of two bodies upon each other are always equal in magnitude and directed along opposite directions. Vector representation: $$\vec{F}_{AB} = -\vec{F}_{BA}$$ where $\vec{F}_{AB}$ … Read more
Concept Card: Linear Momentum & Newton’s Second Law of Motion 1. Linear Momentum ($\vec{p}$): The linear momentum $\vec{p}$ of a body of mass $m$ moving with velocity $\vec{v}$ is defined as: $\vec{p} = m\vec{v}$ – Vector quantity; directed along the velocity vector $\vec{v}$. – SI unit: $\text{kg}\cdot\text{m/s}$ or $\text{N}\cdot\text{s}$. Dimensions: $[M L T^{-1}]$. Relation with … Read more
Concept Card: Force, Inertia & Newton’s First Law of Motion 1. Physical Definition and Nature of Force: A force is an external vector interaction (push or pull) that changes or tends to change an object’s state of rest or of uniform rectilinear motion, or causes deformation. Forces in nature are classified fundamentally into four categories: … Read more
Concept Card: Projectile Motion on an Inclined Plane & Uniform Circular Motion Part A: Projectile Motion on an Inclined Plane 1. Coordinate Frame Transformation: Orient the coordinate axes relative to the incline: – $+x’$ axis: Directed up along the surface of the incline. – $+y’$ axis: Directed perpendicular (normal) to the incline. Let the inclination … Read more
Concept Card: Oblique Projectile Motion 1. Physical Framework & Initial Conditions: A particle launched from ground level with initial speed $u$ at an angle of elevation $\theta$ ($0 < \theta < 90^\circ$) to the horizontal moves in a vertical plane under the constant downward acceleration of gravity $\vec{g}$. Taking the launch point as origin $O(0, ... Read more
Concept Card: Horizontal Projectile Motion 1. Physical Framework & Coordinate Setup: A projectile launched horizontally with initial speed $u$ from a height $h$ above level ground moves under the sole influence of gravity (neglecting air resistance). Choosing the point of projection as the origin $O(0, 0)$, with the horizontal forward direction as $+x$ and the … Read more
Concept Card: Motion in a Plane & 2D Kinematics 1. Position and Displacement Vectors in Two Dimensions (2D): In a Cartesian coordinate plane ($x-y$), the position of a particle at time $t$ is represented by the position vector $\vec{r}(t)$ directed from origin $O$ to point $P(x, y)$: Position Vector: $\vec{r}(t) = x(t)\hat{i} + y(t)\hat{j}$ Magnitude: … Read more
Concept Card: Relative Velocity in Two Dimensions (River-Boat & Rain-Man) 1. Fundamental Formulation of 2D Relative Velocity: The velocity of object $A$ observed from the frame of reference of object $B$ is given by vector subtraction: $\vec{v}_{AB} = \vec{v}_A – \vec{v}_B$ $\vec{v}_A = \vec{v}_{AB} + \vec{v}_B$ where $\vec{v}_A$ and $\vec{v}_B$ are measured relative to a … Read more
Concept Card: Vectors & Vector Algebra (Addition & Subtraction) 1. Scalars vs. Vectors: Scalar Quantity: A physical quantity completely specified by a numerical magnitude (number + unit) and sign. It obeys the ordinary rules of algebra. Examples: Mass, time, distance, speed, work, energy, temperature, electric charge. Vector Quantity: A physical quantity possessing both magnitude and … Read more
Concept Card: Master Review & Strategy Sheet for 1D Kinematics 1. The Calculus Backbone of Kinematics: When acceleration is non-constant, kinematic formulas cannot be applied directly; calculus definitions must be used: Velocity: $v(t) = \frac{dx}{dt} \iff x(t) = x_0 + \int_{0}^{t} v(t’)\,dt’$ Acceleration (Time Form): $a(t) = \frac{dv}{dt} = \frac{d^2 x}{dt^2} \iff v(t) = u … Read more