Motion in a Plane Class 11 Notes Class 11 CBSE

Ch-3 Motion in a Plane

Topic Covered

–Latest CBSE syllabus 2024-2025

-Introduction, Two Dimensional Motion

-Vectors, Types of Vector 

-Triangle Law of Vector Addition, Parallelogram Law of Vector Addition.

-Projectile Motion, Time of Flight, Horizontal Range, Maximum height, Path or Trajectory of Projectile.

-Uniform Circular Motion, Angular Displacement, Angular Velocity, Angular Acceleration

-Centripetal Acceleration.

-All types of Numericals Based on CBSE, JEE, NEET, NDA. 

Motion in a Plane class 11 notes

Motion in two dimensions, such as projectile motion, circular motion, etc., is referred to as motion in a plane. Our reference points for the investigation of this motion will be the origin and the two coordinate axes, X and Y.
• Quantities, Scalar and Vector
Quantities that are Scalar. Scalar quantities are those physical quantities that can be fully described by their size or magnitude alone.

Instances: length, mass, density, velocity, etc.
Vector Measurements. Physical quantities that have both magnitude and direction are known as vector quantities.
Examples include force, momentum, torque, acceleration, displacement, and velocity.

• Vector Characteristics
The qualities of vectors are as follows:
(i) They have both direction and magnitude.
(ii) These defy the standard algebraic laws.
(iii) These alter if changes occur in either the direction or magnitude.
(iv) Boldfaced letters or letters with an arrow over them are used to symbolise these.
• Vector Unit
A unit vector is a vector with a specific direction and magnitude. It is simply used to indicate the direction. A cap (^) is used to indicate a unit vector over the amount.

The Law of Parallelogram Vector Addition
The diagonal of the parallelogram that passes through the point completely represents the resultant in both magnitude and direction if two vectors acting simultaneously at a point can be represented in both directions by the two adjacent sides of a parallelogram drawn from that point.

The Law of Triangle Vector Addition
When two vectors are represented by the two sides of a triangle taken in the same order for both magnitude and direction, the resultant of these vectors is represented by the third side of the triangle taken in the opposite order for both magnitude and direction.

• The Law of Polygonal Vector Addition
When the sides of a polygon taken in the same order indicate multiple vectors in both magnitude and direction, the closing side of the polygon taken in the opposite order represents the resultant vector in both directions and magnitude.

• Vector Resolution
It is the act of dividing a single vector into two or more vectors that, when combined, go in separate directions and yield the same result as the original vector alone.
Components of vectors are the vectors into which the supplied single vector is divided. In actuality, a vector’s resolution and composition are exactly the opposite.

• Projectile Motion (Motion in a Plane class 11 notes)
An object that is given an initial inclination velocity and then follows a course dictated by both the air’s frictional resistance and the gravitational force acting upon it is referred to as a projectile. A projectile’s trajectory is the path it travels.
Projectile motion equation. An item with a starting velocity of u at an angle of 8 above (or below) the horizontal is the general case of projectile motion. The displacements x and y, both horizontal and vertical, are determined by

• Angular Displacement (Motion in a Plane class 11 notes)

The angle that the radius vector at the circular path’s centre sketched out in a specific amount of time is the definition of the object’s angular displacement when moving along it.
θ (angle) = arc/radius θ —> the angular displacement magnitude. Radians (rad) are used to express it.
• The angle of velocity
The time rate of change of an object’s angular displacement is known as its angular velocity when it is moving in a circular path.

• Uniform Circular Motion (Motion in a Plane class 11 notes)

A body is said to be moving in uniform circular motion when it travels in a circle at a steady speed.
Time period is the amount of time an object takes to complete one revolution on its circular route. The frequency (v) of circular motion is the total number of revolutions made in a given amount of time. One hertz is the unit of frequency (1 Hz). It is discovered that

• Centripetal Acceleration  (Motion in a Plane class 11 notes)

A constant radially inward acceleration is necessary to keep a particle moving in a uniform circle. The centripetal acceleration is the name given to it.