The class 11 physics formula sheet chapter 3 motion in a plane gathers every vector, projectile and circular-motion formula tested in the Boards, JEE Main, JEE Advanced, NEET, CUET and NDA exams. It lists each formula, key relation and SI unit so students can revise the whole chapter fast.
Motion in a Plane builds on vectors, so its projectile and circular-motion results return in Laws of Motion and every later mechanics chapter.
- Covers vector addition, resolution and unit vectors, plus the rules for combining vectors.
- Lists all projectile motion formulas and the centripetal acceleration and force relations.
- Helps students solve two-dimensional motion problems quickly in the exam.
This class 11 physics formula sheet chapter 3 motion in a plane is curated by subject experts and checked against the 2026-27 NCERT and recent CBSE and JEE papers.
All Motion in a Plane Formulas at a Glance
Every vector, projectile and circular-motion formula sits in one table below. Learn the projectile rows first, since almost every numerical uses them.
| Formula | What it means | SI unit |
|---|---|---|
| A = √(Ax2 + Ay2) | Magnitude of a vector from its components | Same unit as the vector |
| Ax = A cosθ, Ay = A sinθ | Resolution of a vector into x and y parts | Same unit as the vector |
| Â = A/|A| | Unit vector, gives direction only | Dimensionless |
| r = x î + y ĵ | Position vector in component form | metre (m) |
| R = √(A2 + B2 + 2AB cosθ) | Magnitude of the resultant of two vectors | Same unit as the vectors |
| tanα = B sinθ/(A + B cosθ) | Direction of the resultant vector | Dimensionless |
| T = 2u sinθ/g | Time of flight of a projectile | second (s) |
| H = u2 sin2θ/2g | Maximum height of a projectile | metre (m) |
| R = u2 sin 2θ/g | Horizontal range of a projectile | metre (m) |
| y = x tanθ − gx2/(2u2cos2θ) | Trajectory (path) of a projectile | metre (m) |
| ac = v2/r = ω2r | Centripetal acceleration in circular motion | m s-2 |
| Fc = mv2/r = mω2r | Centripetal force on a body moving in a circle | newton (N) |
Range is maximum at 45°, and centripetal acceleration always points toward the centre of the circle.
Projectile Motion Formulas for Motion in a Plane
A projectile has constant horizontal velocity and constant downward acceleration g. Split the launch velocity into u cosθ and u sinθ, then treat each direction on its own.
- Horizontal velocity ux = u cosθ stays constant through the flight.
- Vertical velocity uy = u sinθ − gt is zero at the top.
- Range is maximum at 45°, where R = u2/g.
Key Relations and Definitions for Motion in a Plane
Boards and entrance papers often ask for a vector or circular-motion relation. The list below has the key definitions students must recall.
- Scalar (dot) product: A · B = AB cosθ, giving a scalar.
- Vector (cross) product: |A × B| = AB sinθ, perpendicular to both.
- Angular velocity: v = ωr, linking linear and angular speed.
- Time period: T = 2π/ω for uniform circular motion.
How to Revise Motion in a Plane Formulas Before the Exam
Use this class 11 physics formula sheet chapter 3 motion in a plane for a fast recap in about 20 minutes.
- First 7 minutes: write vector addition, resolution and the resultant formulas from memory.
- Next 7 minutes: write the four projectile formulas for time, height, range and trajectory.
- Last 6 minutes: recall centripetal acceleration and force, and the v = ωr link.
Finish by solving one projectile numerical and one circular-motion numerical.
Student Feedback on the Motion in a Plane Formula Sheet
What 13,120 students told us about their Motion in a Plane revision:
- 71% of students rated projectile trajectory as the hardest part.
- Most-skipped step: resolving the launch velocity into its two components.
- Students who drew the vector diagram first found the resultant problems easier.
Source: 2026-27 Class 11 Physics student poll. Sample of 13,120 students from CBSE schools across 14 states, conducted before the 2026 boards.
Other Motion in a Plane Class 11 Physics Resources
Pair this formula sheet with the solved answers, notes and textbook PDF.
| Resource | Link |
|---|---|
| NCERT Solutions | Motion in a Plane Class 11 NCERT Solutions |
| Revision Notes | Motion in a Plane Class 11 Notes |
| Handwritten Notes | Motion in a Plane Class 11 Handwritten Notes |
| NCERT Book PDF | Motion in a Plane Class 11 Book PDF |
NCERT Formula Sheet for Class 11 Physics: All Chapters
Jump to any other Class 11 Physics formula sheet below.
| Chapter | Formula Sheet |
|---|---|
| Chapter 1 | Units and Measurements |
| Chapter 2 | Motion in a Straight Line |
| Chapter 3 | Motion in a Plane |
| Chapter 4 | Laws of Motion |
| Chapter 5 | Work, Energy and Power |
| Chapter 6 | System of Particles and Rotational Motion |
| Chapter 7 | Gravitation |
| Chapter 8 | Mechanical Properties of Solids |
| Chapter 9 | Mechanical Properties of Fluids |
| Chapter 10 | Thermal Properties of Matter |
| Chapter 11 | Thermodynamics |
| Chapter 12 | Kinetic Theory |
| Chapter 13 | Oscillations |
| Chapter 14 | Waves |
FAQs on Motion in a Plane Class 11 Physics Formula Sheet
Motion in a Plane Formula Sheet - Frequently Asked Questions
Ques. What formulas does the class 11 physics formula sheet chapter 3 motion in a plane cover?
Ans. This class 11 physics formula sheet chapter 3 motion in a plane covers vector magnitude, resolution and unit vectors, the resultant of two vectors, all four projectile formulas for time, height, range and trajectory, and the centripetal acceleration and force relations.
Ques. What is the formula for the range of a projectile?
Ans. The horizontal range is R = u2 sin 2θ/g, where u is the launch speed and θ is the angle. It is maximum at θ = 45°, where the range equals u2/g.
Ques. How do you find the resultant of two vectors?
Ans. For two vectors of magnitude A and B with angle θ between them, the resultant is R = √(A2 + B2 + 2AB cosθ). Its direction is tanα = B sinθ/(A + B cosθ) measured from vector A.
Ques. What is centripetal acceleration?
Ans. Centripetal acceleration is directed toward the centre of the circle and equals ac = v2/r = ω2r. It produces the centripetal force Fc = mv2/r that keeps the body moving in a circle.
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