Class 11 Physics Motion in a Plane Notes

Class 11 Physics Motion in a Plane Notes

Scalar and Vector Quantities

Scalar Quantities

  • Have only magnitude
  • No direction

Examples: distance, speed, mass, time

Vector Quantities

  • Have both magnitude and direction

Examples: displacement, velocity, acceleration, force

🔹 Representation of Vectors

A vector is represented by a directed line segment:

  • Length → magnitude
  • Arrow → direction

🔹 Types of Vectors

  • Zero vector – magnitude is zero
  • Unit vector – magnitude is one
  • Equal vectors – same magnitude and direction
  • Negative vectors – same magnitude, opposite direction

🔹 Unit Vector

A unit vector represents the direction of a vector.A^=A⃗∣A⃗∣\hat{A} = \frac{\vec{A}}{|\vec{A}|}A^=∣A∣A​

Common unit vectors:

  • i^\hat{i}i^ along x-axis
  • j^\hat{j}j^​ along y-axis
  • k^\hat{k}k^ along z-axis

🔹 Addition of Vectors

1️⃣ Triangle Law of Vector Addition

If two vectors are represented by two sides of a triangle taken in order, the third side represents their resultant.

2️⃣ Parallelogram Law

If two vectors act at a point, the diagonal of the parallelogram gives the resultant vector.

🔹 Resolution of Vectors

Breaking a vector into components along x and y directions.Ax=Acos⁡θA_x = A \cos\thetaAx​=Acosθ Ay=Asin⁡θA_y = A \sin\thetaAy​=Asinθ

🔹 Motion in a Plane

Motion in which an object moves in two dimensions.

Examples:

  • Projectile motion
  • Circular motion

🔹 Projectile Motion

Motion of an object thrown into the air under gravity.

Important Points:

  • Horizontal velocity remains constant
  • Vertical motion is affected by gravity
  • Path followed is a parabola

Time of Flight:

T=2usin⁡θgT = \frac{2u\sin\theta}{g}T=g2usinθ​

Maximum Height:

H=u2sin⁡2θ2gH = \frac{u^2\sin^2\theta}{2g}H=2gu2sin2θ​

Range:

R=u2sin⁡2θgR = \frac{u^2\sin2\theta}{g}R=gu2sin2θ​

🔹 Uniform Circular Motion

Motion of an object in a circular path with constant speed.

Key Points:

  • Velocity direction changes continuously
  • Acceleration is directed towards the center (centripetal acceleration)

a=v2ra = \frac{v^2}{r}a=rv2​

🔹 Relative Velocity in Two Dimensions

Velocity of one object with respect to another when both are moving in a plane.

Used in:

  • River-boat problems
  • Aircraft-wind problems