Chapter 3 — Motion in a Plane

Chapter 3 of the Class 11 Physics NCERT textbook, "Motion in a Plane", covers motion in two dimensions using vector algebra, including projectile motion and uniform circular motion. Download the free NCERT PDF.

• Vectors as the language of 2D motion — Describing motion in a plane needs vectors, which carry both magnitude and direction. The chapter builds the toolkit—addition, resolution into perpendicular components, and analytical methods—so any plane motion can be handled through its parts.
• Splitting motion into independent axes — A central strategy is treating plane motion as two independent one-dimensional motions along x and y. This reduces complex 2D problems to familiar straight-line kinematics applied separately in each direction.
• Projectile and circular motion — The methods explain projectile motion as a parabolic path from combined horizontal and vertical motion, and uniform circular motion where a centre-directed acceleration continually turns the velocity while keeping speed constant.

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.