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Have you ever watched a bird change direction mid-flight or seen a football curve through the air after a powerful kick? These real-life examples involve motion in a plane when an object moves in two dimensions. In These NCERT notes you will learn how to analyze and describe such motion using vectors and basic math tools.
NCERT Notes for Class 11 Physics Chapter 3: Motion in a Plane are very helpful if you are trying to score well in physics. In the last chapter, we looked at motion in a straight line using plus and minus signs to show direction. But in real life, things don’t just move in a straight line they move in all sorts of directions. That is where vectors come in. Vectors help us explain motion when both direction and size matter, like with speed, force, or displacement. To do well in exams, it is important to understand each topic properly and practice the NCERT questions at the end of the chapter. These NCERT Notes for class 11 are prepared by our expert faculty based on the latest CBSE syllabus.
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NCERT Notes on Class 11 Physics Chapter 3 Motion in a Plane gives a precise and concise description of two-dimensional motion, vectors, projectile motion and uniform circular motion. These notes can be used to revise the concepts instantly and prepare the objective exams such as CBSE, JEE, and NEET.
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:
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
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.
A position vector is a vector that represents the location of a point or a particle in space with respect to a fixed origin. It is usually denoted by
If a particle is located at point
A displacement vector represents the change in position of a particle. It is defined as the vector that points from the initial position to the final position of the object.
If the position vector of the initial point is
Displacement is a vector quantity, having both magnitude and direction, and is independent of the actual path taken.
Two vectors are said to be equal if they have the same magnitude and same direction, regardless of their initial points.
That is, if
then
This means that vectors can be moved parallel to themselves in space without changing their properties, as long as magnitude and direction are preserved.
If
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).
(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.
To subtract vector
Scalar Product (Dot Product): The scalar product or dot product of two vectors
Vector Product (Cross Product): The vector product or cross product of two vectors
Resolution of a vector is the process of expressing a single vector as the sum of two or more vectors (called components), usually along mutually perpendicular directions (like the
If a vector
Thus, the vector
Let two vectors
Then the resultant vector
Now, the magnitude of the resultant vector is:
And the direction (angle
In motion in a plane, the position, velocity, and acceleration of an object are all described using vectors.
The motion can be analyzed by breaking it into two perpendicular directions, usually the
The position vector of an object at any instant is given by:
The velocity vector is the time derivative of the position vector:
The acceleration vector is the derivative of velocity:
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
1. Time of flight ( T ):
2. Maximum height(h):
3. Horizontal range(R):
4. Maximum horizontal range(
Note: For maximum range, θ should be 45 degrees.
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.
Horizontal Motion | Vertical Motion |
When an object moves in a circular path with constant speed, the motion is called Uniform Circular Motion (UCM). Although the speed remains constant, the direction of velocity changes continuously, making it an accelerated motion.
Angular Velocity:
Relation between
Centripetal Acceleration:
Centripetal Force:
A unit vector is a vector with a magnitude of 1, commonly denoted by a hat symbol (), used to represent direction without affecting magnitude
Yes, Motion in a Plane Class 11 notes are useful for JEE (Joint Entrance Examination) preparation. These notes cover essential concepts from the CBSE Physics Syllabus and can serve as a valuable resource for understanding and revising key topics related to motion in a plane. JEE often includes questions that require a strong foundation in physics, and having comprehensive notes can aid in effective preparation for the examination.
The following statement is correct: "A displacement vector is a location vector." In class 11th physics chapter 4 notes the position or condition of any point that is similar to the position vector is represented by a displacement vector. To some extent, the position and displacement vectors are comparable. The displacement vector differs from the position vector in that it describes the position of any point in relation to other points rather than the origin. The position vector, on the other hand, specifies the position of any point in relation to the origin. This is how the truth of the statement is demonstrated.
A bird turning mid-air, a car taking a curved turn, or a football following a curved path after a kick all show motion in two dimensions, which this chapter helps you understand.
It explains how objects move in two dimensions using vectors. You'll learn about projectile motion, circular motion, and how to handle direction and magnitude together.
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