Motion in a Plane Class 11 Notes CBSE Physics Chapter 4 [Free PDF Download] (2022)

1. Scalars and Vectors:

Some quantities can be described by a unique number. For example, mass, time, distance and speed can be described using a single number. These are called scalar quantities.

To express to someone how to get to a location from some other location, one piece of information is not enough. To describe this fully, both distance and displacement are required.

Quantities that require both magnitude and direction to describe a situation fully are known as vectors. For example, displacement and velocity are vectors.

The vectors are denoted by putting an arrow over the symbols representing them.

For example, AB vector can be represented by $\overrightarrow{AB}$.

1.1 Unit Vector:

A unit vector has a magnitude of one and hence, it actually gives just the direction of the vector.

A unit vector can be determined by dividing the original vector by its magnitude

$\Rightarrow \hat{a}=\frac{{\vec{a}}}{\left| {\vec{a}} \right|}$

Unit vectors along different co–ordinate axis are as shown below:

(Image will be updated soon)

1.2 Addition, subtraction and scalar multiplication of vectors:

Consider two vectors as follows:

\[{{\vec{r}}_{1}}={{a}_{1}}\hat{i}+{{b}_{1}}\hat{j}\]

\[{{\vec{r}}_{2}}={{a}_{2}}\hat{i}+{{b}_{2}}\hat{j}\]

Then,

\[{{\vec{r}}_{1}}+{{\vec{r}}_{2}}=\left( {{a}_{1}}+{{a}_{2}} \right)\hat{i}+\left( {{b}_{1}}+{{b}_{2}} \right)\hat{j}\]

\[{{\vec{r}}_{1}}-{{\vec{r}}_{2}}=\left( {{a}_{1}}-{{a}_{2}} \right)\hat{i}+\left( {{b}_{1}}-{{b}_{2}} \right)\hat{j}\]

Multiplication of a vector by scalar quantity:

\[c{{\vec{r}}_{1}}=c\left( {{a}_{1}}\hat{i}+{{b}_{1}}\hat{j} \right)=c{{a}_{1}}\hat{i}+c{{b}_{1}}\hat{j}\]

Representation of ${{\vec{r}}_{1}}$ on the co–ordinate axis:

(Image will be updated soon)

Magnitude and direction of ${{\vec{r}}_{1}}$:

Magnitude of ${{\vec{r}}_{1}}\left( \left| {{{\vec{r}}}_{1}} \right| \right)=\sqrt{{{a}_{1}}^{2}+{{b}_{1}}^{2}}$

Direction of ${{\vec{r}}_{1}}$ is given by

$\tan \theta =\frac{{{b}_{1}}}{{{a}_{1}}}=\frac{component\text{ }y-axis}{component\text{ }along\text{ }x-axis}$

$\Rightarrow \theta ={{\tan }^{-1}}\left( \frac{{{b}_{1}}}{{{a}_{1}}} \right)$

1.3 Parallel vectors:

Two vectors are said to be parallel vectors if and only if they have the same direction. When any vector is multiplied by a scalar, a vector parallel to the original vector is obtained.

If $b=ka$, then b and a are parallel vectors. Generally, to find if two vectors are parallel or not, we should find their unit vectors.

1.4 Equality of vectors:

Two vectors (representing two values of the same physical quantity) are referred to as equal if their corresponding magnitudes and directions are the same.

For example, $\left( 3i+4j \right)m\,\,and\,\,\left( 3i+4j \right)\frac{m}{s}$ cannot be compared as they represent two different physical quantities.

1.5 Addition of vectors:

When two or more vectors are added, the answer is referred to as the resultant. The resultant of two vectors is equivalent to the first vector followed immediately by the second vector.

(Image will be updated soon)

To determine the resultant of vectors a and b, the tail of vector b should be joined to the head of vector a. The resultant a+b is nothing but the direct vector from the tail of vector a to the head of vector b as shown below.

(Image will be updated soon)

This is known as triangle rule of vector addition. Another way to obtain the resultant vector is parallelogram rule of vector addition. Here, we draw vectors \[\vec{a}\] and \[\vec{b}\], with both the tails coinciding. Taking these two as adjacent sides of a parallelogram, we complete the parallelogram. Now, the diagonal through the common tails gives the sum of two vectors.

(Image will be updated soon)

Finding the magnitude of \[\vec{a}+\vec{b}\] and its direction:

\[{{\left| AD \right|}^{2}}=A{{E}^{2}}+E{{D}^{2}}\text{ }\]

Here,

$AE=\left| {\vec{a}} \right|+\left| b\,\cos \,\theta \right|$

$ED=b\,\sin \,\theta $

$\Rightarrow A{{D}^{2}}={{a}^{2}}+{{b}^{2}}{{\cos }^{2}}\theta +2ab\cos \theta +{{b}^{2}}{{\sin }^{2}}\theta $

$\Rightarrow A{{D}^{2}}={{a}^{2}}+{{b}^{2}}+2ab\cos \theta $

$\Rightarrow AD=\sqrt{{{a}^{2}}+{{b}^{2}}+2ab\cos \theta }$

where,

(Video) MOTION IN A PLANE | CLASS 11th | PHYSICS CHAPTER-4 | BEST HANDWRITTEN NOTES

$\theta $is the angle contained between \[\vec{a}\] and \[\vec{b}\];

Also,

$\tan \alpha =\frac{ED}{AE}=\frac{b\,\sin \theta }{a+b\cos \theta }$

where,

$\alpha $ is the angle which the resultant makes with the positive x-axis.

Subtraction of vectors:

Let \[\vec{a}\] and \[\vec{b}\] be two vectors. We define \[\vec{a}-\vec{b}\] as the sum of vectors $\vec{a}$ and the vector$(-\vec{b})$.

$\Rightarrow \vec{a}-\vec{b}=\vec{a}+(-\vec{b})$

(Image will be updated soon)

Zero vector:

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In the given triangle, \[\overrightarrow{PQ}+\overrightarrow{QR}+\overrightarrow{PR}\] should be equal to zero as the overall journey results in a return to the starting point.

\[\Rightarrow \overrightarrow{PQ}+\overrightarrow{QR}+\overrightarrow{PR}=0\]

Here are some other resultants:

(Image will be updated soon)

Here, $\vec{a}+\vec{b}+\vec{c}+\vec{d}+\vec{e}=0\Rightarrow \vec{e}=-(\vec{a}+\vec{b}+\vec{c}+\vec{d})$

(Image will be updated soon)

Here, $\vec{a}+\vec{b}+\vec{c}=0$

Resolution of vectors:

(Image will be updated soon)

Consider the given diagram above.

Here,

\[\overrightarrow{OA}=\vec{a}\]

By vector addition rule,

\[\overrightarrow{OA}=\overrightarrow{OB}+\overrightarrow{OC}\]

$\left| \overrightarrow{OB} \right|=a\cos \,\theta $

$\left| \overrightarrow{OC} \right|=a\,\sin \theta $

If $\hat{i}$ and $\hat{j}$ denote vectors of unit magnitude along OX and along OY respectively, we get

$\overrightarrow{OB}=a\,\cos \theta \,\hat{i}$

$\overrightarrow{OC}=a\,\sin \theta \,\hat{j}$

$\Rightarrow \vec{a}=\left( a\,\cos \theta \right)\hat{i}+\left( a\,\sin \theta \right)\hat{j}$

(Image will be updated soon)

1.6 Dot product or scalar product of two vectors:

(Image will be updated soon)

Dot product of vectors $\vec{a}$ and $\vec{b}$ is given by

$\vec{a}.\vec{b}=\left| {\vec{a}} \right|\left| {\vec{b}} \right|\,\cos \theta $

If $\theta =0;$

$\Rightarrow \vec{a}.\vec{b}=\left| {\vec{a}} \right|\left| {\vec{b}} \right|\,$

If $\theta ={{90}^{\circ }}$;

$\Rightarrow \vec{a}.\vec{b}=\left| {\vec{a}} \right|\left| {\vec{b}} \right|\,{{90}^{\circ }}=0$

Dot product of unit vectors are given by

$\hat{i}\cdot \hat{i}=\left| {\hat{i}} \right|\left| {\hat{i}} \right|\,\cos {{0}^{\circ }}={{i}^{2}}\times 1=1$

Similarly,

$\hat{j}\cdot \hat{j}=1$;

$\hat{k}\cdot \,\hat{k}=1$

Now,

$\hat{i}\cdot \hat{j}=\left| {\hat{i}} \right|\left| {\hat{j}} \right|\,\cos {{90}^{\circ }}=1\times 1\times 0=0$

Similarly,

$\hat{j}\cdot \hat{k}=0\,$;

$\hat{k}\cdot \hat{i}=0$

Dot products are commutative and distributive:

\[\vec{a}\cdot \vec{b}=\vec{b}\cdot \vec{a}\]

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\[\vec{a}\cdot \left( \vec{b}+\vec{c} \right)=\vec{a}\cdot \vec{b}+\vec{a}\cdot \vec{c}\]

2. MOTION IN 2D (PLANE)

2.1 Position vector and Displacement:

The position vector $\vec{r}$ of a particle P, located in a plane with reference to the origin of on xy–coordinate system is given by $\vec{r}=x\hat{i}+y\hat{j}$, as shown below.

(Image will be updated soon)

Now, if the particle moves along the path as shown to a new position ${{P}_{1}}$ with the position vector ${{\vec{r}}_{1}}$;

${{\vec{r}}_{1}}={{x}_{1}}\hat{i}+{{y}_{1}}\hat{j}$

Change in position of the particle is nothing but its displacement given by,

$\Delta \vec{r}={{\vec{r}}_{1}}-\vec{r}=\left( {{x}_{1}}\hat{i}+{{y}_{1}}\hat{j} \right)-\left( x\hat{i}+y\hat{j} \right)$

$\Rightarrow \Delta \vec{r}==\left( {{x}_{1}}-x \right)\hat{i}+\left( {{y}_{1}}-y \right)\hat{j}$

$\Delta \vec{r}==\Delta x\hat{i}+\Delta y\hat{j}$

From the figure, it can also be seen that

\[\vec{r}+\Delta \vec{r}={{\vec{r}}_{1}}\,\,\,\,\,\,\,or\,\,\,\,\,\Delta \vec{r}={{\vec{r}}_{1}}-\,\,\vec{r}\], which is nothing but the triangle law of vector addition.

2.2 Average velocity:

Average velocity is given by,

${{\vec{v}}_{avg}}=\frac{\Delta \vec{r}}{\Delta t}=\frac{\Delta x\hat{i}+\Delta y\hat{j}}{\Delta t}$

$\Rightarrow {{\vec{v}}_{avg}}={{v}_{x}}\hat{i}+{{v}_{y}}\hat{j}$

Note: Direction of the average velocity is the same as that of \[\Delta \vec{r}\].

2.3 Instantaneous velocity:

Instantaneous velocity is given by,

$\vec{v}=\underset{\Delta t\to 0}{\mathop{\lim }}\,\frac{\Delta v}{\Delta t}=\frac{d\vec{r}}{dt}$

$\Rightarrow \vec{v}={{v}_{x}}\hat{i}+{{v}_{y}}\hat{j}$

(Image will be updated soon)

Here,

${{v}_{x}}=\frac{dx}{dt}\,\,and\,\,{{v}_{y}}=\frac{dy}{dt}$

$\Rightarrow \left| {\vec{v}} \right|=\sqrt{{{v}_{x}}^{2}+{{v}_{y}}^{2}}$

Also,

$\tan \theta =\frac{{{v}_{y}}}{{{v}_{x}}}$

$\Rightarrow \theta ={{\tan }^{-1}}\left( \frac{{{v}_{y}}}{{{v}_{x}}} \right)$

Note: The direction of instantaneous velocity at any point on the path of an object is the tangent to the path at that point and is in the direction of motion.

2.4 Average acceleration:

$\theta ={{\tan }^{-1}}\left( \frac{{{v}_{y}}}{{{v}_{x}}} \right)$Average acceleration is given by,

${{\vec{a}}_{avg}}=\frac{\Delta \vec{v}}{\Delta t}=\frac{\Delta {{v}_{x}}}{\Delta t}\hat{i}+\frac{\Delta {{v}_{y}}}{\Delta t}\hat{j}$

$\Rightarrow {{\vec{a}}_{avg}}={{a}_{x}}\hat{i}+{{a}_{y}}\hat{j}$

2.5 Instantaneous acceleration:

Instantaneous acceleration is given by,

\[\vec{a}=\frac{dv}{dt}=\frac{d{{v}_{x}}}{dt}\hat{i}+\frac{d{{v}_{y}}}{dt}\hat{j}\]

\[\Rightarrow \vec{a}={{a}_{x}}\hat{i}+{{a}_{y}}\hat{j}\]

3. PROJECTILE MOTION:

When a particle is projected obliquely close to the surface of the earth, it moves simultaneously in horizontal and vertical directions. Motion of such a particle is referred to as projectile motion.

(Image will be updated soon)

Here, a particle is projected at an angle with an initial velocity ‘u’.

Considering the projectile motion given in the diagram above, let us calculate the following:

(a) time taken to reach A from O

(b) horizontal distance covered (OA)

(c) maximum height reached during the motion

(d) velocity at any time ‘t’ during the motion

Horizontal axis

Vertical axis

${{u}_{x}}=u\,\cos \,\theta $

${{a}_{x}}=0$

(In the absence of any external force, \[{{a}_{x}}\]would be assumed to be zero).

${{u}_{y}}=\,u\,\sin \,\theta $

${{a}_{y}}=-g$

${{s}_{y}}={{u}_{y}}t+\frac{1}{2}{{a}_{y}}{{t}^{2}}$

$\Rightarrow 0-0=u\,\sin \,\theta t-\frac{1}{2g{{t}^{2}}}$

$\Rightarrow $

${{s}_{x}}={{u}_{x}}t+\frac{1}{2{{a}_{x}}{{t}^{2}}}$

$\Rightarrow x-0=u\,\cos \theta \,t$

$\Rightarrow x=u\,\cos \,\theta \,\times 2u\sqrt{g}$

$\Rightarrow x=\frac{2{{u}^{2}}\,\cos \theta \sin \theta }{g}$

$\Rightarrow $

\[\left( \because 2cos\theta sin\theta =\text{ }sin2\theta \right)\]

Horizontal distance covered is known as Range (R).


${{v}_{y}}={{u}_{y}}+{{a}_{y}}t$

$$

It depends on time ‘t’.

It is not constant.

It’s magnitude first decreases; becomes zero

and then increases.

${{v}_{x}}={{u}_{x}}+{{a}_{x}}t$

$$

It is independent of t.

It is constant.

Time of ascent and time of descent:

At the top most point, ${{v}_{y}}=0$

${{v}_{y}}={{u}_{y}}+{{a}_{y}}t$

$\Rightarrow 0=u\,\sin \theta -gt$

$\Rightarrow {{t}_{1}}=\frac{u\sin \theta }{g}$

$\Rightarrow {{t}_{2}}=T-{{t}_{1}}=\frac{u\,\sin \theta }{g}$

$\Rightarrow $

Maximum height obtained by the particle

Method 1: Using time of ascent;

${{s}_{y}}={{u}_{y}}{{t}_{1}}+\frac{1}{2}ay{{t}_{1}}^{2}$

$\Rightarrow $

Method 2: Using third equation of motion

${{v}_{y}}^{2}-{{u}_{y}}^{2}=2{{a}_{y}}{{s}_{y}}$

$\Rightarrow 0-{{u}^{2}}\,{{\sin }^{2}}\theta =-2g{{s}_{y}}$

$\Rightarrow $

Maximum Range:

$R=\frac{{{u}^{2}}\sin 2\theta }{g}\,\,and\,\,{{R}_{\max }}=\frac{{{u}^{2}}}{g}$

Range is maximum when $\sin 2\theta $ is maximum;

$\Rightarrow \max \left( \sin 2\theta \right)=1\,\text{ }or\text{ }\theta ={{45}^{\circ }}$

3.1 Analysis of velocity in case of a projectile:

(Image will be updated soon)

(Video) Motion in a plane physics class 11 (Vectors) Full chapter handwritten notes

From the above equations;

i) ${{v}_{1x}}={{v}_{2x}}={{v}_{3x}}={{v}_{4x}}={{u}_{x}}=u\,\cos \theta $

which suggests that the velocity along x axis remains constant.

[as there is no external force acting along that direction]

ii)

a) The magnitude of velocity along y axis first decreases and then it increases after the top most point.

b) At the top most point, magnitude of velocity is zero.

c) Direction of velocity is in the upward direction while ascending and is in the downward direction while descending.

d) Magnitude of velocity at A is the same as magnitude of velocity at O; but the directions are opposite.

e) Angle which the net velocity makes with the horizontal can be evaluated by,

$\tan \alpha =\frac{{{v}_{y}}}{{{v}_{x}}}=\frac{velocity\text{ }along\text{ }y\text{ }axis}{velocity\text{ }along\text{ }x\text{ }axis}$

f) Net velocity is always along the tangent.

3.2 Equation of trajectory:

Trajectory refers to the path traced by the body. To determine the trajectory, we should find the relation between y and x by eliminating time.

(Image will be updated soon)

Horizontal Motion

Vertical Motion

${{u}_{x}}=u\,\cos \theta $

${{a}_{x}}=0$

${{s}_{x}}=u\,\cos \,\theta \,t=x$

$\Rightarrow t=\frac{x}{u\,\cos \,\theta }$

${{u}_{y}}=u\,\sin \,\theta $

${{a}_{y}}=-g$

${{s}_{y}}={{u}_{y}}t+\frac{1}{2}{{a}_{y}}{{t}^{2}}$

$\Rightarrow y=u\,\sin \theta \left( \frac{x}{u\,\cos \,\theta } \right)-\frac{1}{2}g\frac{{{x}^{2}}}{{{u}^{2}}{{\cos }^{2}}\theta }$

$$

(i) This is the equation of a parabola.

(ii) Because the coefficient of ${{x}_{2}}$ is negative, it is an inverted parabola.

(Image will be updated soon)

Path of the projectile is a parabola.

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

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

Substituting this value in the above equation, we have,

$\Rightarrow $

4. RELATIVE MOTION:

Relativity is a very common term. In physics, we use relativity very oftenly.

For example, consider a moving car and yourself (observer) as shown below.

(Image will be updated soon)

Case I: If you are observing a car moving on a straight road, then you say that the velocity of car is 20m/s; which means that velocity of car relative to you is 20m/s; or, velocity of car relative to the ground is 20m/s (as you are standing on the ground.

Case II: If you go inside this car and observe, you would find that the car is at rest while the road is moving backwards. Then, you would say, the velocity of the car relative to the car is 0m/s.

Mathematically, velocity of B relative to A is represented as

${{\vec{v}}_{BA}}={{\vec{v}}_{B}}-{{\vec{v}}_{A}}$

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

$\therefore \,\,{{\vec{v}}_{BA}}\ne {{\vec{v}}_{AB}}$

5. RIVERBOAT PROBLEMS:

In riverboat problems, we come across the following three terms:

${{\vec{v}}_{r}}=$ absolute velocity of river.

${{\vec{v}}_{br}}=$ velocity of a boatman with respect to river or velocity of a boatman in still water, and

${{\vec{v}}_{b}}=$ absolute velocity of boatman.

Clearly, it is important to note that ${{\vec{v}}_{br}}$ is the velocity of a boatman with which he steers and ${{\vec{v}}_{b}}$ is the actual velocity of boatman relative to ground. Further,

${{\vec{v}}_{b}}={{\vec{v}}_{br}}+{{\vec{v}}_{r}}$

Now, let us derive a few standard results and their special cases.

A boatman starts from point A on one bank of a river with velocity ${{\vec{v}}_{br}}$ in the direction shown in figure. River is flowing along positive x-direction with velocity ${{\vec{v}}_{r}}$. Width of the river is ‘d’. Then,

${{\vec{v}}_{b}}={{\vec{v}}_{br}}+{{\vec{v}}_{r}}$

Therefore,

${{v}_{bx}}={{v}_{rx}}+{{v}_{brx}}={{v}_{r}}-{{v}_{br}}\sin \theta $

And

${{v}_{by}}={{v}_{by}}+{{v}_{bry}}=0+{{v}_{br}}\cos \theta ={{v}_{br}}\cos \theta $

(Image will be updated soon)

Now, the time taken by the boatman to cross the river is given by,

$t=\frac{d}{{{v}_{by}}}=\frac{d}{{{v}_{br}}\cos \theta }\,$

$\Rightarrow t=\frac{d}{{{v}_{br}}\cos \theta }\,\,\,$…(1)

Further, displacement along the x-axis when he reaches on the other bank (also called as drift) is given by,

(Video) Class 11th Physics Chapter 4 Motion in a Plane | Hand written Notes 📒|Air Force, NDA, Navy|

$x={{v}_{bx}}t=\left( {{v}_{r}}-{{v}_{br}}\sin \theta \right)\frac{d}{{{v}_{br}}\cos \theta }$

\[\Rightarrow x=\left( {{v}_{r}}-{{v}_{br}}\sin \theta \right)\frac{d}{{{v}_{br}}\cos \theta }\]…(2)

Condition when the boatman crosses the river in shortest interval of time:

From (1), it can be seen that time (t) will be minimum when $\theta =\text{ }0{}^\circ $ i.e., the boatman should steer his boat perpendicular to the river current.

Condition when the boat wants to reach point B, i.e., at a point just opposite from where he started (shortest distance):

In this case, the drift (x) should be zero.

$\Rightarrow x=0$

$\Rightarrow \left( {{v}_{r}}-{{v}_{br}}\sin \theta \right)\frac{d}{{{v}_{br}}\cos \theta }=0$

$\Rightarrow {{v}_{r}}={{v}_{br}}\sin \theta $

$\Rightarrow \sin \theta =\frac{{{v}_{r}}}{{{v}_{br}}}\,$

$\Rightarrow \theta ={{\sin }^{-1}}\left( \frac{{{v}_{r}}}{{{v}_{br}}} \right)$

Clearly, to reach point B, the boatman should row at an angle $\theta ={{\sin }^{-1}}\left( \frac{{{v}_{r}}}{{{v}_{br}}} \right)$ upstream from AB.

Now, time is given by,

$t=\frac{d}{{{v}_{b}}}=\frac{d}{\sqrt{{{v}_{br}}^{2}-{{v}_{r}}^{2}}}$

As $\sin \theta $ is not greater than 1 and when \[{{v}_{r}}\ge {{v}_{br}}\], then the boatman can never reach at point B.

Because, when \[{{v}_{r}}=\text{ }{{v}_{br}}\], \[\sin \theta ~=1\] or $\sin \theta =90{}^\circ $ and it is just impossible to reach at B if $\theta =90{}^\circ $.

Similarly, when \[{{v}_{r}}>{{v}_{br}}\], \[sin\theta ~>1\], i.e., no such angle exists. Practically, it can be realized in this manner that it is not possible to reach at B if the river velocity (${{v}_{r}}$) is too high.

6. RELATIVE VELOCITY OF RAIN WITH RESPECT TO A MOVING MAN:

Consider a man walking west with velocity ${{\vec{v}}_{m}}$, represented by OA. Let the rain be falling vertically downwards with velocity ${{\vec{v}}_{r}}$, represented by OB, as shown in the following figure. To find the relative velocity of rain with respect to man (i.e.,${{\vec{v}}_{rm}}$) assume the man to be at rest by imposing a velocity $-{{\vec{v}}_{m}}$ on the man and apply this velocity on rain also. Now, the relative velocity of rain with respect to man would be the resultant velocity of ${{\vec{v}}_{r}}(=\overrightarrow{OB})$ and $-{{\vec{v}}_{m}}\left( =\overrightarrow{OC} \right)$, which would be represented by the diagonal OD of rectangle OBDC.

$\Rightarrow {{v}_{rm}}=\sqrt{{{v}_{r}}^{2}+{{v}_{m}}^{2}+2{{v}_{r}}{{v}_{m}}\cos {{90}^{\circ }}}=\sqrt{{{v}_{r}}^{2}+{{v}_{m}}^{2}}$

(Image will be updated soon)

If $\theta $is the angle which ${{v}_{rm}}$makes with the vertical direction, then

$\tan \theta =\frac{BD}{OB}=\frac{{{v}_{m}}}{{{v}_{r}}}$

$\Rightarrow \theta ={{\tan }^{-1}}\left( \frac{{{v}_{m}}}{{{v}_{r}}} \right)$

Here, angle $\theta $ is from the vertical towards west and is written as $\theta $, west of vertical.

Note: In the above problem, if the man wants to protect himself from the rain, he should hold his umbrella in the direction of relative velocity of rain with respect to man. i.e., the umbrella must be held making an angle \[~\left( \theta =ta{{n}^{1}}\left( \frac{{{v}_{m}}}{{{v}_{r}}} \right) \right)\], west of the vertical.

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Notes of Physics Class 11 Chapter 4: Important Discussions

Motion in a Plane comprises some important topics which are discussed below, students might take a note of these topics:

Introduction to Plane Motion

The very first section of Class 11 Physics Notes Chapter 4 deals with the meanings of velocity, acceleration and magnitude. Know about the various terms and their definitions in Physics by studying the Motion in a Plane Class 11 Notes.

Motion in a Plane

Here, students will get to know about different motions in a plane like circular motion, projectile motion, etc. Besides, application of motion in a straight line’s equations are applied in x and y directions to find out the motion in a plane’s equations are also described in Motion in a Plane Class 11 Notes.

Projectile Motion

By studying from Physics Ch 4 Class 11 Notes, you will get a clear idea about projectile motion (a special type of motion in a plane). Various projectile motion examples are also provided in the Motion in a Plane Class 11 Notes.

Scalars and Vectors

Along with the definitions of scalar and vector quantities, this section of Physics Class 11 Notes discusses differences and characteristics between the two. Furthermore, explanations of unit vectors, equal vectors, zero vectors, negative of a vector, parallel vectors, displacement vectors and coplanar vectors are also given in Motion in a Plane Class 11 Notes.

Resolution of Vectors, and Addition and Subtraction of Vectors

In this section of Class 11 Physics Notes Chapter 4, students will get enlightened how a vector can be resolved and what is the process of resolution all about. Specifically in the world of Physics, vectors are resolved as per x, y and z coordinates. Next comes the techniques of addition and subtraction of vectors. Both geometrical and analytical methods are discussed in detail in Motion in a Plane Class 11 Notes, assisting you to have a proper grasp over the same.

2D Relative Velocity

This section in Chapter 4 Physics Class 11 Notes starts with the explanation of relative motion velocity. Following which you will get to study 2D relative motion velocity in the Motion in a Plane Class 11 Notes, which is elucidated with a precise and straightforward derivation.

Uniform Circular Motion

The final section of Motion in a Plane Class 11 Notes focusses on uniform circular motion along with the descriptions of variables used in the same, for instance, angular displacement, angular acceleration, angular velocity and centripetal acceleration. Later in this segment of Class 11th Physics Chapter 4 Notes, more about projectile motion are elaborated comprising 2D projectiles, essential pointers of projectile motion, etc.

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FAQs

What is motion in a plane Class 11 notes? ›

Motion in a plane is called as motion in two dimensions e.g., projectile motion, circular motion etc. For the analysis of such motion our reference will be made of an origin and two co-ordinate axes X and Y. Scalar Quantities.

What is the name of Chapter 4 in physics class 11? ›

NCERT Solutions for Class 11 Physics Chapter 4 Motion In A Plane.

What is motion in 2d Class 11? ›

When the object travels in x and y coordinates with a constant velocity, it is known as two-dimensional motion.

What are the important topics in motion in a plane? ›

Important Topics of Motion in a Plane

Resolution of Vectors. Motion in a plane with constant acceleration. Relative Velocity in Two dimensions. Projectile Motion.

What is scalar and vector quantity? ›

A quantity that has magnitude but no particular direction is described as scalar. A quantity that has magnitude and acts in a particular direction is described as vector.

What is a vector class 11 physics? ›

The quantities which have both magnitude and direction are called vectors. Examples are velocity, force, displacement, weight, acceleration, etc. The quantities which have only magnitude and no direction are called scalar quantities.

What is arbitrary motion? ›

Arbitrary motion refers to oscillations that grow or decay at a specific frequency. It can be interpreted as a random direction used to refer to some motion. It is not required to produce anything from that direction. It has nothing to do with the direction in such questions about arbitrary motion.

What is circular motion class XI? ›

Circular motion is a motion in which a body travels a definite distance along a circular path.

What is the fourth equation of motion? ›

or v2 = u2 + 2as and this equation of motion can be used to find the final velocity or the distance travelled if the other values are given.

What is 3d motion? ›

Motion in three dimension: Motion in space which incorporates all the X, Y and Z axis is called three dimensional motion. Example: Movement of gyroscope is an example of three dimensional motion.

What is measure of inertia? ›

Measurement of inertia

Mass is a quantitative measure of a body's inertia. Mass is the amount of matter present in a body. inertia is proportional to mass. If mass increases, then inertial will increase. If we have an idea about the mass of a body, then inertia can be measured.

Is kinematics 1d important for JEE? ›

Kinematics is considered an important as well as an easy chapter of Mechanics that is a part of the JEE Mains syllabus.

Is motion in a plane important for NEET? ›

Important notes of Physics for NEET, JEE for Motion in a Plane are useful for all aspirants preparing for entrance exams including JEE, NEET. Important notes are also helpful for revision when you have less time and have to study many topics.

What is a two dimensional motion? ›

Two-dimensional (2D) motion means motion that takes place in two different directions (or coordinates) at the same time. The simplest motion would be an object moving linearly in one dimension. An example of linear movement would be a car moving along a straight road or a ball thrown straight up from the ground.

What are the types of motion in a plane? ›

Motion in a Plane. Motion in a plane is also referred to as a motion in two dimensions. For example, circular motion, projectile motion, etc. For the analysis of such type of motion, the reference point will be made of an origin and the two coordinate axes X and Y.

What is the SI unit of velocity? ›

The SI unit of velocity is metre per second (m/s).

Is force a vector or scalar? ›

Force is not a scalar quantity. Force is a vector quantity, as it has both direction and magnitude.

Is force a vector? ›

A force has both magnitude and direction, therefore: Force is a vector quantity; its units are newtons, N.

Is vector important for NEET? ›

Vectors are a very important topic in Physics for NEET as well as for the board exams. It is covered very well in the Class 11 Physics NCERT textbook. Make sure you are through with that particular chapter.

Is vectors important for JEE? ›

Vectors occupy an extremely important place in IIT JEE preparation. It accounts for 5% of the JEE screening. For majority of students,vectors is the most interesting topic encountered by them in JEE Mathematics. The best part is that it also fetches good number of questions in JEE.

How do you write a zero vector? ›

A zero vector or a null vector is defined as a vector in space that has a magnitude equal to 0 and an undefined direction. Zero vector symbol is given by →0=(0,0,0) 0 → = ( 0 , 0 , 0 ) in three dimensional space and in a two-dimensional space, it written as →0=(0,0) 0 → = ( 0 , 0 ) .

What is arbitrary shape? ›

Definition. The Arbitrary shape (constant width/height) discontinuity represents a microwave circuit that is constant along a certain direction, but is otherwise arbitrary in the normal plane.

What is arbitrary angle? ›

An arbitrary angle is of an unspecified and insignificant size. It is an angle whose size does not matter for the purposes of the particular question being considered.

What is arbitrary ray? ›

Arbitrary ray, characterized by the direction of the normalized wave vector K ˆ I , incident upon the corner-cube. Source publication. Ray trace through a corner-cube retroreflector with complex reflection coefficients. Article.

What is the SI unit of acceleration? ›

Acceleration (a) is defined as the rate of change of velocity. Velocity is a vector quantity, and therefore acceleration is also a vector quantity. The SI unit of acceleration is metres/second2 (m/s2).

What is circular motion formula? ›

The instantaneous acceleration in a uniform circular motion is given by. a = v2/R. v is the velocity of the object. R is the radius of the circle. The direction is perpendicular to velocity and directed inwards along the radius.

What is the 2nd equation of motion? ›

The second equation of motion gives the displacement of an object under constant acceleration: x = x 0 + v 0 t + 1 2 a t 2 .

What is the first equation of motion? ›

The first equation of motion, v = u + at is referred to as the velocity-time relation. On the other hand, the second equation of motion is s = ut + 1 / 2at2 can be called the position-time relation. Likewise, we call the third equation of motion, v2 = u2+ 2as, position – velocity relation.

What is 3D anime called? ›

3D animation, also referred to as CGI, or just CG, is made by generating images using computers. That series of images are the frames of an animated shot.

What are the 5 types of animation? ›

5 Forms of Animation
  • Traditional Animation.
  • 2D Animation.
  • 3D Animation.
  • Motion Graphics.
  • Stop Motion.

What is a 4D animation? ›

April 2022) 4D film is a high technology multisensory presentation system combining motion pictures with physical effects that are synchronized and occur in the theatre. Effects simulated in 4D films include motion, vibration, scent, rain, mist, bubbles, fog, smoke, wind, temperature changes, and strobe lights.

Is inertia a force? ›

Inertia is the force that holds the universe together. Literally. Without it, matter would lack the electric forces necessary to form its current arrangement. Inertia is counteracted by the heat and kinetic energy produced by moving particles.

What is the SI unit of momentum? ›

SI Unit of Momentum

As mentioned above, the units of momentum will be the product of the units of mass and velocity. Mass is measured in kg and velocity in ms-1, therefore, the SI unit of momentum will be kgm/s(-1).

Is inertia a mass? ›

Mass is one type of inertia. Inertia is a general term for an object's resistance against acceleration (or against change in its velocity). In linear (translational) cases, the inertia is called mass m.

Is kinematics Class 11 hard? ›

Kinematics is one of the easiest and important chapters of Mechanics in the syllabus of IIT JEE, AIEEE and other engineering examinations.

Is 2d motion important for JEE? ›

Two-dimensional motion is an important concept that is used to describe displacement, acceleration, speed, etc. It is the change in motion of an object with time.

Are kinematics tough? ›

The kinematics portion can be considered difficult but it is still possible to do well in this subject as long as you study well and study with the right materials.

Why is horizontal velocity zero? ›

Suppose the particle in projectile motion reaches its highest point along the horizontal path. In that case, the horizontal velocity will usually be zero because as soon as it reaches the peak point, it is made to fall vertically downwards by the influence of the force of gravity.

What is a point object? ›

In kinematics, a point object is an expression. It is an object whose dimensions are overlooked or ignored in comparison to its movement. A point object is a tiny object that is counted as a dot object to simplify calculations.

What are the types of motion? ›

According to the nature of the movement, motion is classified into three types as follows: Linear Motion. Rotary Motion. Oscillatory Motion.

What is velocity on a plane? ›

A positive velocity is defined to be toward the tail of the aircraft. The airspeed can be directly measured on the aircraft by use of a pitot tube. For a reference point picked on the aircraft, the ground moves aft at some velocity called the ground speed.

What is the formula of time of flight? ›

Time of flight

t ( v 0 sin θ 0 − g t 2 ) = 0. Ttof=2(v0sinθ0)g. T tof = 2 ( v 0 sin θ 0 ) g . This is the time of flight for a projectile both launched and impacting on a flat horizontal surface.

What is space motion? ›

1. : the motion of the earth and other solar system members as they travel through space with the sun. : space velocity.

What is motion in a plane? ›

Motion in a plane is also referred to as a motion in two dimensions. For example, circular motion, projectile motion, etc. For the analysis of such type of motion, the reference point will be made of an origin and the two coordinate axes X and Y.

What is motion class 11? ›

If an object changes its position with respect to its surroundings with time, then it is called in motion.

What is projectile motion class 11? ›

Projectile motion : Projectile motion is a form of motion in which object or particle ( called a projectile , is thrown near earth's surface and it moves along a curved path under the action of gravity only.

Why do we need vectors Class 11? ›

Vectors are the most basic and important part of Calculus. We represent 3-dimensional space using vectors. We do 3D geometry completely using the properties of vectors. Any problem in science which has to deal with the direction component has to be done with the help of vectors.

What are the 4 types of motions? ›

The four types of motion are:
  • linear.
  • rotary.
  • reciprocating.
  • oscillating.

What is velocity on a plane? ›

A positive velocity is defined to be toward the tail of the aircraft. The airspeed can be directly measured on the aircraft by use of a pitot tube. For a reference point picked on the aircraft, the ground moves aft at some velocity called the ground speed.

Is kinematics 1d important for JEE? ›

Kinematics is considered an important as well as an easy chapter of Mechanics that is a part of the JEE Mains syllabus.

What are the 3 equation of motion? ›

The following are the three equation of motion: First Equation of Motion: v = u + at. Second Equation of Motion: s = ut + 1/2(at2) Third Equation of Motion: v2 = u2 – 2as.

Is straight line a motion? ›

Motion in a straight line is called straight motion. If the direction of a moving object is constant and the object is moving at a constant speed, then it is moving in a straight line. In this case, the object is said to be moving in a straight line at constant speed.

What is rest motion? ›

Rest and Motion Definitions

Rest: An object is said to be at rest if it does not change its position with respect to its surroundings with time. Motion: An object is said to be in motion if the position changes with respect to it surrounding and time.

What are the 3 types of projectile motion? ›

The following are the three types of projectile motion: Horizontal projectile motion. Oblique projectile motion. Projectile motion on an inclined plane.

What are the 2 types of projectile motion? ›

There are the two components of the projectile's motion - horizontal and vertical motion.

What is flight time formula? ›

Time of flight

t ( v 0 sin θ 0 − g t 2 ) = 0. Ttof=2(v0sinθ0)g. T tof = 2 ( v 0 sin θ 0 ) g . This is the time of flight for a projectile both launched and impacting on a flat horizontal surface.

Why do we use vector? ›

Vectors are used in science to describe anything that has both a direction and a magnitude. They are usually drawn as pointed arrows, the length of which represents the vector's magnitude.

Why is a vector important? ›

In physics, vectors are useful because they can visually represent position, displacement, velocity and acceleration. When drawing vectors, you often do not have enough space to draw them to the scale they are representing, so it is important to denote somewhere what scale they are being drawn at.

Why is vector important in real life? ›

Vectors have many real-life applications, including situations involving force or velocity. For example, consider the forces acting on a boat crossing a river. The boat's motor generates a force in one direction, and the current of the river generates a force in another direction.

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3. Motion in a Plane Class 11 Notes - Arjuna Batch || Motion in a Plane Class 11 Notes Physics Wallah
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