NCERT Class 11 Physics Chapter 4 Motion in a Plane Notes - Download PDF

Hey there! Ever wondered how things move in all directions? Well, CBSE Class 11 Physics Chapter 3 has got you covered with the awesome topic "Motion in a Plane." We're diving into forces, acceleration, and displacement—what's cool about them is that they don’t just move in numbers but also directions!

This chapter is super important for exams, and we've got some handy Motion in a Plane notes for CBSE Class 11 that are not only easy to understand but also available for free in PDF format! These notes are like cheat codes for figuring out how forces and movements work in all directions.

So, if you're ready for a fun and simple physics adventure, grab your notes, and let’s make learning Motion in a Plane super easy! It's physics made simple and stress-free.

Also, students can refer,

• NCERT Solutions for Class 11 Physics Chapter 3 Motion in a Plane
• NCERT Exemplar Class 11 Physics Chapter 3 Motion in a Plane

Scalars And Vectors

Scalar

• A scalar has only magnitude (size).

• You get it by multiplying the number with the unit of the quantity.

• Examples: Mass, Speed, Distance

• You can add, subtract, and multiply scalars using simple math.

Vector

• A vector has both magnitude and direction.

• They follow the rules of vector addition like: $\vec{A}+\vec{B}=\vec{B}+\vec{A}$ and the law of parallelogram addition.

• Examples: Displacement, Velocity, Acceleration, Force
• The magnitude of a vector is represented by $|\vec{A}|$ or $A$. Vectors are shown with an arrow.

Representation of vector

• A vector looks like a line with an arrow.

• The length of the arrow shows the magnitude.

• The direction of the arrow shows the direction of the vector.

A vector can be represented geometrically as a directed line segment with an arrowhead. The arrow's length represents the magnitude of the vector, and it points in the same direction as the vector itself.Tail $\underset{\text { (magnitude) }}{\xrightarrow{\text { Length }}}$ Head

Types of Vector

• Equal vectors: If the magnitudes and directions of vectors A and B are the same, they are equal.
• Parallel vectors are A and B when: 1. They both point in the same direction. 2. Two vectors can be expressed as scalar (positive) non-zero multiples of each other.
• Antiparallel vectors: A and B are anti-parallel if their directions are opposite.
  - One vector is a negative multiple of the other that is not zero.
  - A vector with 0 magnitude and an arbitrary (unknown) direction is called a zero vector.

• Unit vector: A unit vector is a vector with a fixed magnitude that points in a specific direction. A vector (A) can be expressed as the product of a unit vector (Â) in its direction and magnitude.

$\vec{A}=A \hat{A} \quad$ or $\quad \hat{A}=\frac{\vec{A}}{A}$

A unit vector has no dimensions or units. Unit vectors along the positive x, y, and z axes of a rectangular coordinate system are denoted by î, ˆ j, and k̂, respectively. such that $|\hat{\mathbf{i}}|=|\hat{\mathbf{j}}|=|\hat{\mathbf{k}}|=1$

Addition of Vectors

Either the triangle law or the parallelogram law can be used to add vectors:

(A) Parallelogram law of addition of vectors: The diagonal drawn through the intersection of two vectors, A and B, represents the resultant vector if they are represented by two adjacent sides of a parallelogram, both pointing outward from a common point (with their tails coinciding).

$R=\sqrt{P^2+Q^2+2 P Q \cos \theta}$

(B) The Triangle Law of Vector Addition states that if two vectors are represented by two triangle sides, then the third side of the triangle represents their total or resultant vector, but in the opposite direction.

Multiplication of Vectors

Scalar Product (Dot Product): The scalar product or dot product of two vectors $\vec{A}$ and $\vec{B}$, denoted as $\vec{A} \cdot \vec{B}$ , is defined as the product of their magnitudes multiplied by the cosine of the angle (θ) between them. Mathematically, it is expressed as:

$\vec{a} \cdot \vec{b}=a_x b_x+a_y b_y+a_z b_z=a b \cos \theta$

Vector Product (Cross Product): The vector product or cross product of two vectors $\vec{A}$ and $\vec{B}$, denoted as $\vec{A} X \vec{B}$ B, is a vector quantity defined as follows:

$\begin{gathered}\vec{a} \times \vec{b}=\left(a_y b_z-a_z b_y\right) \hat{\imath}+\left(a_z b_x-a_x b_z\right) \hat{\jmath}+\left(a_x b_y-a_y b_x\right) \hat{k} \\ |\vec{a} \times \vec{b}|=a b \sin \theta\end{gathered}$

Lami’s Theorem: Lami's Theorem states that each force is proportional to the sine of the angle generated by the other two forces if three forces operating at the same spot are in equilibrium.

$\frac{F_1}{\sin \alpha}=\frac{F_2}{\sin \beta}=\frac{F_3}{\sin \gamma}$

Projectile Motion

A body that is propelled with some initial velocity—not including vertical upward or downward motion—is called a projectile. Once in motion, the projectile moves only due to gravity; it is not further propelled by an engine, fuel, or other external source. A projectile's trajectory is the course it takes while in motion.

• For motion along the X-axis,

$
v_x=u_x+a_x t \text { and } x=x_0+u_x t+\frac{1}{2} a_x t^2
$

- For motion along $\underline{\mathrm{Y} \text {-axis, }}$

$
v_y=u_y+a_y t \text { and } y=y_0+u_y t+\frac{1}{2} a_y t^2
$

• Angular projection of projectile :

1. Time of flight ( T ):

$\mathrm{T}=\frac{2 u \sin \theta}{g}$

2. Maximum height(h):

$h=\frac{u^2 \sin ^2 \theta}{2 g}$

3. Horizontal range(R):

$\mathrm{R}=\frac{u^2 \sin 2 \theta}{g}$

4. Maximum horizontal range( $\mathrm{R}_{\max }$ ):

$R_{\max }=\frac{u^2}{g} \text { for } \theta=45^{\circ}$

Note: For maximum range, θ should be 45 degrees.

Equation of trajectory

A trajectory is the term used to describe the body's journey. We must determine the link between y and x and eliminate time in order to build the trajectory.

Relative Motion

Observing the motion of one item from the viewpoint of another is known as relative motion. It is the study of how an item moves when seen from a different perspective.

Case I: Saying that a car is travelling at 20 mph when on a straight road indicates that the vehicle is moving at that speed either in relation to you or to the ground (as you stand on the ground).

Case II: This automobile is at a halt while the road is travelling backward, as you can see if you peek inside. The automobile's velocity relative to the car would then be 0 m/s.

The velocity of B about A is expressed mathematically as

$v_{B A}=v_B-v_A$
$\therefore \vec{v}_{B A} \neq \vec{v}_{A B}$

Riverboat problems

We come across the following three terms when dealing with riverboat issues:

v_r^'= the river's absolute velocity

v_br^'= a boatman's velocity about the river, or a boatman's velocity in still water

v_b^'= boatman’s absolute velocity

$v_b=v_{b r}+v_r$

Why Motion in a Plane Notes Class 11 is Important

• Builds the Basics for Higher Classes:
  This chapter is like the foundation for many tough topics you'll study later—like 3D motion and advanced vectors.

• Useful in Real Life:
  Many things around us move in two dimensions—like balls in sports, cars on roads, or planets in space. Learning this topic helps you understand how these motions work.

• Improves Problem-Solving Skills:
  You’ll work with vectors, angles, components, and math tricks. This sharpens your thinking and helps in solving tougher physics and engineering problems.

• Covers Projectile Motion:
  Motion in a plane includes learning about projectile motion—like how a cricket ball moves when thrown. It’s super useful in sports, designing machines, and engineering.

• Leads into Circular Motion:
  You'll also get a taste of circular motion here, which is important for things like fans, wheels, and satellites. This link makes it easier to understand other topics later.

• Important for Science & Engineering:
  This chapter is a must-know for those planning to go into fields like engineering, space science, or robotics. Topics like fluid flow and satellite orbits are based on this.

Significance of NCERT Class 11 Physics Chapter 3 Notes

Class 11 notes are useful for going over the chapter again and understanding important ideas. Since they cover key subjects from the CBSE Physics Syllabus, these NCERT Class 11 Physics chapter 3 notes are helpful for competitive tests like VITEEE, BITSAT, JEE Main, and NEET. Studying offline is made easier by the PDF format.

• Quick Revision Tool:
  These notes help you revise the entire chapter quickly before exams or tests. Everything important is summarized in one place.

• Time-Saving:
  Instead of going through the whole textbook again, you can refer to these notes to save time while preparing.

• Boosts Understanding:
  Complex concepts like vector addition, projectile motion, and motion in two dimensions are explained in simple language, making learning easier.

• Perfect for Exam Preparation:
  These notes highlight important formulas, laws (like Lami's theorem), and definitions that are commonly asked in exams.

• Builds Conceptual Clarity:
  Class 11 Physics is all about strong concepts. These notes help you understand the "why" and "how" behind every concept, not just the "what".

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