Chapter 4: Motion in a Plane – Quick Revision Notes 1. Introduction Motion in one dimension (straight-line motion) involves a single axis (x or y). Motion in two dimensions (motion in a plane) involves both x and y axes (e.g., projectile motion). The position of an object in a plane is described using vector notation. --- 2. Scalars and Vectors Scalar Quantities: Only have magnitude (e.g., distance, speed, time, mass). Vector Quantities: Have both magnitude and direction (e.g., displacement, velocity, acceleration, force). Vector Representation: Represented by an arrow; the length represents magnitude, and the arrowhead shows direction. Vectors are added using the triangle law or parallelogram law. --- 3. Addition and Subtraction of Vectors Triangle Law: If two vectors are placed tail to head, the resultant is the vector from the free tail to the free head. Parallelogram Law: If two vectors form adjacent sides of a parallelogram, the diagonal represents the resultant. Resolution of Vectors: A vector A can be split into horizontal (Aₓ) and vertical (Aᵧ) components: Aₓ = A cosθ (along x-axis) Aᵧ = A sinθ (along y-axis) The magnitude of A is given by A = √(Aₓ² + Aᵧ²). The direction is θ = tan⁻¹(Aᵧ / Aₓ). --- 4. Motion in Two Dimensions Motion in a plane involves both x and y directions. It can be uniform or accelerated motion. Position Vector (r): r = x î + y ĵ, where (x, y) are coordinates in the plane. Velocity Vector (v): v = vₓ î + vᵧ ĵ Acceleration Vector (a): a = aₓ î + aᵧ ĵ --- 5. Projectile Motion A projectile is an object thrown into the air under gravity, following a curved parabolic path. Motion is analyzed in two parts: Horizontal Motion: Constant velocity (no acceleration). Vertical Motion: Uniformly accelerated motion due to gravity (g = 9.8 m/s²). Equations for Projectile Motion Time of flight (T) = 2u sinθ / g Maximum height (H) = u² sin²θ / 2g Horizontal range (R) = u² sin2θ / g Where: u = initial velocity θ = angle of projection g = acceleration due to gravity At maximum height, vertical velocity becomes zero. The total flight time depends on the initial velocity and angle of projection. --- 6. Uniform Circular Motion An object moving in a circular path with constant speed has uniform circular motion. Velocity is always tangent to the circular path, and acceleration is centripetal, directed toward the center. Centripetal Acceleration: a = v² / r Angular velocity (ω): ω = v / r Centripetal Force: F = m v² / r --- 7. Relative Motion in Two Dimensions When two objects move in different directions, their relative velocity is found using vector subtraction. Relative Velocity Formula: V_AB = V_A - V_B, where V_AB is velocity of A with respect to B. --- Final Exam Tips ✔ Learn and practice vector addition and resolution. ✔ Understand projectile motion formulas and their applications. ✔ Focus on uniform circular motion and centripetal force. ✔ Solve numerical problems on projectile motion and relative velocity. This is a quick revision summary of the chapter. Join for more - https://whatsapp.com/channel/0029Va9492L3QxRv5MtNFF0Y/151