CBSE Class 11 Physics Revision Notes Chapter 4

Class 11 Physics Revision Notes for Chapter 4 – Motion in a Plane

Force, acceleration and displacement are examples of physical quantities that can be expressed by magnitude and direction which come under the chapter of Motion in a Plane. Since Class 11 Physics Chapter 4 is crucial, important questions could be asked in examinations. Hence, being well-prepared is a must. Extramarks Revision Notes prove helpful in such situations due to their simple and easy-to-understand language.

1. SCALARS AND VECTORS:

A specific number can be used to describe some amounts. For instance, a single number can be used to indicate mass, time, distance and speed. We refer to these as scalar quantities.

One piece of information is insufficient to explain to someone how to get to a location from another location. Both distance and displacement are needed to fully express this.

The term “vector” refers to a quantity that must have both magnitude and direction to completely represent a situation. Vectors include things like displacement and velocity.

By placing an arrow above the symbols that symbolise them, vectors are indicated.

For instance, AB→ can be used to denote an AB vector.

1.1 Unit Vector

Since the magnitude of a unit vector is 1, it just indicates the vector’s direction.

By dividing the initial vector by its magnitude, a unit vector can be found.

a =a→ / |a→| 

1.2 Addition, subtraction and scalar multiplication of vectors

If there are two vectors,

r→1=a1i+b1j

r→2 = a2i+b2j

Then, 

r→1+r→2=(a1+a2)i+(b1+b2)j

r→1−r→2=(a1−a2)i+(b1−b2)j

Scalar Multiplication of a vector:

cr→1= c (a1i + b1j) = ca1i + cb1j

Magnitude and direction of r⃗ 1:

Magnitude of r→1(|r→ 1|)=√a12+b12 

Direction of r→1 is given by

tanθ=b1/a1 = component y−axis / component along x−axis 

⇒θ = tan−1 (b1/a1) 

1.3 Parallel vectors

When two vectors have the same direction, they are said to be parallel. Any vector that is multiplied by a scalar creates a new vector that is parallel to the original.

1.4 Equality of vectors

Two vectors (showing two values of the same physical quantity) are said to be equal if their magnitudes and directions match.

1.5 Addition of vectors

The outcome is referred to as the resultant when two or more vectors are added. The first vector is followed immediately by the second vector when two vectors are added together.

2. MOTION IN 2D (PLANE)

2.1 Position vector and Displacement

According to the formula r→ = xi+yj, a particle P’s position vector r, which is placed in a plane with respect to the origin of an x-y coordinate system can be calculated.

Now, assuming the particle travels along the route as depicted to a new point P1 with the position vector r→1;

r→1= x1i + y1j

The particle’s position change is nothing more than its displacement caused by,

Δr→ =r→1− r→ = (x1i + y1j) − (xi+yj)  

⇒Δr→ ==(x1−x)i + (y1−y)j 

Δr→ == Δxi + Δyj 

The triangle law of vector addition:

r→ +Δr–> =r→1 or Δr→ =r→1− r

2.2 Average velocity:

Average velocity is,

vavg→ = Δr→ /Δt = Δxi + Δyj/Δt 

vavg→= vxi + vyj

2.3 Instantaneous velocity:

Instantaneous velocity is,

v→ =limΔt→0 Δv/Δt = dr→/dt 

v→ =vxi+vyj

Here, 

Vx = dx/dt and vy = dy/dt

|v→| =√ vx2 + vy2

Also, 

tan= vy/vx

= tan-1(vy/vx)

2.4 Average acceleration:

= tan−1(vy/vx) 

Average acceleration is,

a→avg =Δv→ /Δt = Δvx/Δti + Δvy/Δtj 

a→ avg = axi + ayj

 

3. PROJECTILE MOTION:

A particle that is launched obliquely close to the earth’s surface moves simultaneously in the horizontal and vertical axes. Such a particle’s motion is referred to as projectile motion.

A particle with an initial velocity of “u” is fired at an angle.

Using the projectile velocity displayed in the example above, let’s calculate the following:

(a) travel time from point O to point A 

(b) horizontal distance travelled (OA)

(c) the highest point achieved while moving.

(d) the velocity at any point in the motion, time t.

Horizontal axis Vertical axis
ux= u cos θ

ax= 0

(In the absence of any external force, ax would be assumed to be zero).

 uy= u sin θ

uy= -g

sy= uyt + ½ ayt²

⇒0-0 = u sinθ t -1/2gt² 
Sx = uxt + 1/ 2axt²

⇒x-0= u cosθ t

⇒x= u cosθ × 2u√g

⇒x= 2u² sinθ cosθ / g

⇒(2cosθ sinθ = sin2θ)

Horizontal distance covered is known as Range (R)

 Vy= Uy + ayt

$$

It depends on time ‘t’.

It is not constant.

Its magnitude first decreases; becomes zero and then increases.
Vx = ux+axt

$$

It is independent of t.

It is constant.

Time of ascent and time of descent:

At the top most point, vy = 0

vy=uy + ayt

⇒0=u sin θ -gt

⇒t1= u sin θ / g

⇒t2= T-t1 = u sin θ / g

 Maximum height obtained by the particle

Method 1: Using time of ascent;

sy= uyt1 + ½ ayt1²

Method 2: Using the third equation of motion

vy² – uy² = 2aysy

 0-u² sin² θ = -2gsy

Maximum Range:

R=u²sin2θ/g and Rmax=u²/g 

Range is maximum when sin2θ is maximum;

⇒max(sin2θ)=1 or θ=45∘

4. RELATIVE MOTION:

Relativity is a well-known concept. It is used quite often in physics.

Consider the following example of a moving car and yourself (observer).

Case I: If you observe an automobile going on a straight road, you say that the velocity of the car is 20m/s; this indicates that the velocity of the car relative to you is 20m/s; or the velocity of the car relative to the ground is 20m/s (since you are standing on the ground).

Case II: You will see that this car is at rest inside while the road is going backwards. In that case, the car’s velocity would be 0 m/s.

Velocity of B relative to A is represented as

v→ BA=v→B−v→A 

This, being a vector quantity, the direction is important.

v→ BA ≠ v→AB 

3.1 Analysis of velocity in case of a projectile

v1x=v2x=v3x=v4x=ux=ucosθ 

Suggests that the velocity along the x-axis remains constant as there is no external force acting along the direction.

  • The magnitude of velocity along the y-axis falls at first, then increases after the topmost point.
  • The magnitude of velocity is zero at the highest point.
  • When ascending, the velocity is in the upward direction; when falling, it is in the downward direction.
  • The magnitude of velocity at A equals the magnitude of velocity at O; however, the directions are opposite.
  • The net velocity’s angle with the horizontal can be calculated using,

tanα=vy/vx=velocity along y axis / velocity along x axis  

  • Net velocity is always perpendicular to the tangent.

5. RIVERBOAT PROBLEMS:

We come across the following terms in riverboat problems.

v→r=  absolute velocity of river.

v→br= velocity of a boatman with respect to river or velocity of a boatman in still water, and 

v→b= absolute velocity of boatman.

v→b = v→br + v→r  

Notes of Physics Class 11 Chapter 4: Overview

Motion in a Plane contains some important concepts which form the basis of many important physics theories. Thus, it is necessary to understand these topics thoroughly. Extramarks Revision Notes for Class 11 Physics Chapter 4 can help students gain a clear understanding of such topics. These notes contain detailed and easy explanations of the given concepts written in an easy to understand and well-structured format for better retention of information.

Introduction to Plane Motion

This section deals with the definitions and basic ideas of the terms magnitude, velocity, acceleration, etc.

Motion in a Plane

Different types of motions in a plane like circular motion, projectile motion, etc are explained in this part. Furthermore, the application of motion in straight line equations in the x and y directions to determine motion in a plane’s equations is also discussed.

Projectile Motion

The projectile motion of a particle is a kind of motion which is projected at an angle. Here, its ideas and equations are discussed along with detailed examples.

Scalars and Vectors

This section of Physics Class 11 addresses the differences and properties of scalar and vector quantities, in addition to their definitions. In this section, explanations of unit vectors, equal vectors, zero vectors, negative of a vector, parallel vectors, displacement vectors and coplanar vectors are also provided.

Resolution of Vectors, and Addition and Subtraction of Vectors

In this part, students will learn how a vector can be resolved and what the resolution process entails. Vectors are resolved as x, y and z coordinates in the domain of Physics. Following that are vector addition and subtraction procedures. Both geometrical and analytical methods are addressed in depth in Extramarks Motion in a Plane Class 11 Notes, allowing you to gain a thorough understanding of the subject.

2D Relative Velocity

The explanation of relative motion velocity begins this portion of Chapter 4 Physics Class 11 Notes. Then, 2D relative motion velocity will be discussed in detail, which is explained with a clear and straightforward derivation.

Uniform Circular Motion

The final section of Motion in a Plane Class 11 Notes focuses on uniform circular motion and the variables involved, such as angular displacement, angular acceleration, angular velocity and centripetal acceleration. Later in this section Chapter 4, more regarding projectile motion is elaborated, including 2D projectiles, important projectile motion pointers and so on.

FAQs (Frequently Asked Questions)

In general, all mechanical devices begin with an input motion and then alter to force to generate an output motion, which can be rotary, linear, oscillating, or reciprocating. To begin, rotational motion occurs when motion occurs around an axis or a fixed joint, such as a wheel. Second, the motion that occurs in a straight line is deemed linear – for example, train movement. Finally, oscillating motion is defined as the forward and backward movement of a fixed axis. Finally, reciprocating motion is defined as repeating back and forth or down and up motion.

A tensor is a physical quantity with no direction. Instead, it has a range of values pointing in distinct directions. As a result, it is neither a scalar nor a vector quantity. A moment of inertia of any object, for example, has no direction but has varying values in different directions. As a result, it is neither a scalar nor a vector quantity. It is an illustration of a tensor. Tensors also include stress, density, strain and refractive index.

In 1-D motion, or one-dimensional motion, the position of any object is specified by a single coordinate. Only one plane out of three planes specifies the movement of an object with regard to the starting point or origin in this sort of motion. Here are a couple such examples: an automobile moving in a straight line, a train moving in a straight line, a man cycling on a straight road, an object falling on the ground in a straight line due to gravitational force.

Only two coordinates represent an object’s position in two-dimensional motion or 2-D motion. Only two planes out of three coordinates or planes indicate the motion of the item with regard to the origin or starting point in this sort of motion. Here are a couple of such examples: Circular bike rides, death well rides, and an object thrown at an angle

The following are the three basic rules of motion: (i) Unless an external force acts on them, all objects or devices move in a straight or linear direction; (ii) the force applied to an item is directly proportional to its mass and acceleration; and (iii) all actions have an equal and opposite reaction.