Schooling · Class 11 · Physics · Motion in a Plane · Chapter on a page
CBSE Class 11 · Physics · NCERT Physics Part-I
Motion in a Plane: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- Scalars and vectors
- Vector addition
- Resolution of vectors
- Position, displacement and velocity…
- Projectile motion
- Equations for projectile
- Uniform circular motion
- Formulas and facts
- Magnitude of resultant of two…
- Aₓ = A cos θ
- For projectile with initial speed u…
- R = u² sin 2θ / g
- H = u² sin² θ / 2g
- T = 2u sin θ / g
- Trajectory equation
- Watch out for
- Adding vector magnitudes directly…
- Using sin θ and cos θ…
- Thinking velocity is constant in…
- Forgetting to convert angles to…
- Believing an object at the highest…
What this chapter is about
This chapter extends your understanding of motion from one dimension to two dimensions. In Class 9 and the previous chapter, you studied objects moving along a straight line. Now you learn to describe motion when an object can move in a plane — forward-backward and left-right, or horizontal and vertical simultaneously. This requires the mathematical tool of vectors.
Key ideas
- Scalars and vectors: Scalars have only magnitude (mass, temperature, speed). Vectors have both magnitude and direction (displacement, velocity, acceleration, force). Vectors obey special rules of addition.
- Vector addition: Two vectors add by the triangle law or parallelogram law. The resultant of vectors A and B at angle θ has magnitude R = √(A² + B² + 2AB cos θ). Vector addition is commutative: A + B = B + A.
- Resolution of vectors: Any vector in a plane can be written as the sum of two perpendicular components. If vector A makes angle θ with the x-axis, then Aₓ = A cos θ and Aᵧ = A sin θ. The magnitude A = √(Aₓ² + Aᵧ²).
- Position, displacement and velocity vectors: Position vector r gives location relative to origin. Displacement is Δr = r₂ − r₁. Average velocity is Δr/Δt. Instantaneous velocity v = dr/dt is tangent to the path.
- Projectile motion: An object launched with initial velocity and moving under gravity alone follows a parabolic path. Horizontal and vertical motions are independent. Horizontal velocity stays constant; vertical velocity changes by g every second.
- Equations for projectile: For launch angle θ and initial speed u: horizontal range R = u² sin 2θ / g, maximum height H = u² sin² θ / 2g, time of flight T = 2u sin θ / g. Maximum range occurs at θ = 45°.
- Uniform circular motion: An object moving in a circle at constant speed has velocity changing direction continuously. This requires an acceleration directed towards the centre, called centripetal acceleration: aᶜ = v²/r = ω²r, where ω is angular speed.
- Angular quantities: Angular displacement θ is measured in radians. Angular velocity ω = dθ/dt. For uniform circular motion, v = ωr and the period T = 2π/ω.
Formulas and facts to remember
- Magnitude of resultant of two vectors A and B at angle θ: R = √(A² + B² + 2AB cos θ)
- Components of vector A at angle θ to x-axis: Aₓ = A cos θ, Aᵧ = A sin θ
- For projectile with initial speed u at angle θ to horizontal:
- Horizontal range: R = u² sin 2θ / g
- Maximum height: H = u² sin² θ / 2g
- Time of flight: T = 2u sin θ / g
- Trajectory equation: y = x tan θ − (g x²) / (2u² cos² θ), which is a parabola
- Centripetal acceleration for circular motion: aᶜ = v²/r = ω²r, directed towards centre
- Relation between linear and angular speed: v = ωr
- Period of circular motion: T = 2πr/v = 2π/ω
- One complete revolution = 2π radians = 360°
Common mistakes
- Adding vector magnitudes directly without considering direction → Use the parallelogram law or component method; magnitudes add directly only when vectors are in the same direction.
- Using sin θ and cos θ interchangeably in projectile formulas → Remember: vertical component uses sin θ, horizontal component uses cos θ.
- Thinking velocity is constant in uniform circular motion → Speed is constant, but velocity changes direction continuously, so there is acceleration.
- Forgetting to convert angles to radians when using ω → Angular speed ω must be in rad/s for the formula v = ωr to give v in m/s.
- Believing an object at the highest point of its trajectory has zero acceleration → Acceleration due to gravity acts throughout the flight; at the top, only vertical velocity is zero.
Quick revision
- Vectors have magnitude and direction; add them using components or the parallelogram law.
- Projectile motion is two independent motions: constant horizontal velocity and uniformly accelerated vertical motion under gravity.
- Maximum range of a projectile occurs at 45° launch angle (for level ground).
- In uniform circular motion, speed is constant but velocity is not; centripetal acceleration aᶜ = v²/r points towards the centre.
- Always resolve vectors into perpendicular components before adding or using equations of motion.