Class 11 Physics Motion In A Plane

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Section NameTopic Name
4Motion in a plane
4.1Introduction
4.2Scalars and vectors
4.3Multiplication of vectors by real numbers
4.4Addition and subtraction of vectors – graphical method
4.5Resolution of vectors
4.6Vector addition – analytical method
4.7Motion in a plane
4.8Motion in a plane with constant acceleration
4.9Relative velocity in two dimensions
4.10Projectile motion
4.11Uniform circular motion
motion in a plane class 11 notes

NCERT Solutions for Class 11 Physics Chapter 4 Motion in a plane

Class 11 Physics Chapter 4 Motion in a Plane

This chapter you will learn about measuring motion in a plane as well as vector and scalar quantities. You will also get to learn about diagrammatic representation of derivative laws for the addition of vector and scalar quantities. There are topics like displacement and position vector, equality of vectors, vector multiplication by real numbers, the addition of vectors through analytical methods are the topics that will be discussed in this chapter.

Motion In A Plane Notes For Exam

Scalars Vs. Vectors

CriteriaScalarVector
DefinitionA scalar is a quantity with magnitude only.A vector is a quantity with magnitude and direction.
DirectionNoYes
Specified byA number (magnitude) and a unitA number (magnitude), direction and a unit
Represented byquantity’s symbolquantity’s symbol in bold or an arrow sign above
Examplemass, temperaturevelocity, acceleration

Position and Displacement Vectors

Position Vector: Position vector of an object at time t is the position of the object relative to the origin. It is represented by a straight line between the origin and the position at time t.

Displacement Vector: Displacement vector of an object between two points is the straight line between the two points irrespective of the path followed. The path length is always equal or greater than the displacement.

motion in a plane class 11 notes
motion in a plane class 11 notes

Free and Localized Vectors

free vector(or non-localized vector) is a vector of which only the magnitude and direction are specified, not the position or line of action. Displacing it parallel to itself leaves it unchanged.

 A localized vector is a vector where line of action and position are as important as magnitude and direction. These vectors change with change in position and direction.

Equality of Vectors

Two vectors are said to be equal only when they have same direction and magnitude.For example, two cars travelling with same speed in same direction. If they are travelling in opposite directions with same speed, then the vectors are unequal.

Multiplication of Vectors with real numbers

Multiplication FactorOriginal vectorMagnitude of vector after multiplicationDirection of vector after multiplication
λ (>0)AλASame as that of A
-λ (<0)AλAOpposite to that of A
λ (=0)A0 (null vector)None. The initial and final positions coincide.
motion in a plane class 11 notes

Addition and Subtraction of Vectors – Triangle Method

The method of adding vectors graphically is by arranging them so that head of first is touching the tail of second vector and making a triangle by joining the open sides. This method is called head-to-tail method or triangle method of vector addition

motion in a plane class 11 notes
motion in a plane class 11 notes

Addition of Vectors – Parallelogram Method

The method of adding vectors by parallelogram method is by:

  • Touching the tail of the two vectors
  • Complete a parallelogram by drawing lines from the heads of the two vectors.
  • Vector resulting from the origin to the point of intersection of above lines gives the addition.

Unit Vectors

unit vector is a vector of unit magnitude and a particular direction.

  • They specify only direction. They do not have any dimension and unit.
  • In a rectangular coordinate system, the x, y and z axes are represented by unit vectors, î,ĵ andk̂
  • These unit vectors are perpendicular to each other.
  • |î| = |ĵ | = || = 1
motion in a plane class 11 notes
class eleven physics motion in a plane notes
class eleven physics motion in a plane notes
class eleven physics motion in a plane notes
class eleven physics motion in a plane notes

Motion in a plane with constant acceleration

Motion in a plane (two dimensions) can be treated as two separate simultaneous one-dimensional motions with constant acceleration along two perpendicular directions. X and Y directions are hence independent of each other.

If v0 being the velocity at time 0, the displacement can be written as:

x = x+ v0xt+ ½ axt2 and y = y+ v0yt+ ½ ayt2

motion in a plane class 11 notes
motion in a plane class 11 notes

Relative velocity in two dimensions

The concept of relative velocity in a plane is similar to the concept of relative velocity in a straight line.

class eleven physics motion in a plane notes

Projectile Motion

An object that becomes airborne after it is thrown or projected is called projectile. Example, football, javelin throw, etc.

class eleven physics motion in a plane notes
QuantityValue
Components of velocity at time tvx = v0 cosθ0vy = v0 sinθ0–gt
Position at time tx = (v0 cosθ0)ty = (v0 sinθ0)t – ½ gt2
Equation of path of projectile motiony = (tan θ0)x – gx2/2(v0 cosθ0)2
Time of maximum heighttm = v0 sinθ0 /g
Time of flight2 tm = 2 (v0 sinθ0 /g)
Maximum height of projectilehm = (v0 sinθ0)2/2g
Horizontal range of projectileR = v02 sin 2θ0/g
Maximum horizontal range (θ0=45°)Rm = v02/g
motion in a plane class 11 notes
class eleven physics motion in a plane notes

Uniform circular motion

When an object follows a circular path at a constant speed, the motion is called uniform circular motion.

  • Velocity at any point is along the tangent at that point in the direction of motion.
  • Average velocity between two points is always perpendicular to Average displacement. Also, average acceleration is perpendicular to average displacement.
  • For an infinitely small time interval, Δtà 0, the average acceleration becomes instantaneous acceleration which means that in uniform circular motion the acceleration of an object is always directed towards the center. This is called centripetal acceleration.
class eleven physics motion in a plane notes
QuantityValues
Centripetal Accelerationac = v2/R, R – radius of the circleac = ω2R, ω – angular speedac = 4π2ν2R, ν – frequency
Angular DistanceΔθ = ω Δt
Speedv = Rω
motion in a plane class 11 notes
class eleven physics motion in a plane notes

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