Chapter 3 — Motion in a Plane

Class 11 Physics Chapter 3 covers motion in a plane using vector algebra, including projectile motion and uniform circular motion. Download the free NCERT PDF.

Motion in a Plane teaches how to describe 2D motion using vectors. The chapter begins with scalars and vectors, covering vector operations (addition, subtraction, multiplication), resolution of vectors using unit vectors, and analytical methods for vector addition. It then applies these to motion in a plane with constant acceleration, deriving kinematic equations in component form. Projectile motion is analyzed as two independent 1D motions: constant horizontal velocity and vertical motion under gravity. The path follows a parabolic trajectory, with formulas for maximum height, time of flight, and horizontal range. Finally, uniform circular motion explains centripetal acceleration (v²/R) directed toward the center, angular speed (ω = v/R), and the relationship between period, frequency, and linear velocity.

1. 01Vectors have magnitude and direction; scalars have magnitude only. Vector addition follows triangle or parallelogram law, is commutative (A+B=B+A) and associative.
2. 02Any vector can be resolved into components along perpendicular axes using unit vectors î and ĵ. Components relate to magnitude and direction angle by Ax = A cos θ, Ay = A sin θ.
3. 03Motion in a plane is treated as two independent 1D motions. Using r = r₀ + v₀t + ½at² separately for x and y directions simplifies 2D kinematics.
4. 04Projectile motion path is parabolic: y = (tan θ₀)x − gx²/(2v₀² cos² θ₀). Maximum height is hm = (v₀ sin θ₀)²/(2g), reached at time tm = v₀ sin θ₀/g.
5. 05Horizontal range of projectile is R = v₀² sin 2θ₀/g, maximum when θ₀ = 45°. Time of flight is Tf = 2v₀ sin θ₀/g.
6. 06In uniform circular motion, acceleration (centripetal) always points toward center with magnitude ac = v²/R = ω²R, where ω = v/R is angular speed. Velocity remains tangent to the circle.