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# Systems of Particles and Rotational Motion Class 11 Notes CBSE Physics Chapter 6 (Free PDF Download)

Last updated date: 13th Sep 2024
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## Revision Notes for CBSE Class 11 Physics Chapter 6 (System of Particles and Rotational Motion) - Free PDF Download

Notes of chapter 6 system of particles and rotational motion class 11 are available here. Students can download this pdf for free and start their preparations for the final exams. These notes are prepared by our experts with the aim to give an in-depth understanding of the chapter to the students. These notes of chapter 6 physics class 11 are one of the few accurate and reliable study materials available online.

These notes contain comprehensive explanations of each concept. Physics is an observational and application-based study. With better understanding of the concepts, students understand the workings clearly. Also, the new exam pattern requires students to explain the applications of each concept. Students can refer to notes of chapter 6 physics class 11 which explains each concept and its application as well.

## Download CBSE Class 11 Physics Revision Notes 2024-25 PDF

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## System of Particles and Rotational Motion Class 11 Notes Physics - Basic Subjective Questions

### Section-A (1 Mark Questions)

1. A wheel 0.5m in radius is moving with a speed of 12m/s. find its angular speed?

Ans.

$v=r\omega$

$\omega =\dfrac{v}{r}=\dfrac{12}{0\cdot 5}$

$\omega =24\;rad/s$ .

2. State the condition for mechanical equilibrium of a body?

Ans. For mechanical equilibrium of a body the vector sum of all the forces and moments (torques) acting on the body must be zero.

3. How is angular momentum related to linear momentum?

Ans. $\vec{\vec{L}}=\vec{r}\times \vec{p}$

Or L = rp sin θ

Where θ is the angle between $\vec{r}$ and $\vec{p}$ .

4. What is the position of the centre of mass of a uniform triangular lamina?

Ans. Position of the centre of mass of a uniform triangular lamina at the centroid of the triangular lamina.

5. What is the moment of inertia of a sphere of mass 20 kg and radius $\dfrac{1}{4}m$ about its diameter?

Ans. $I=\dfrac{2}{5}MR^{2}$

$I=\dfrac{2}{5}\times 20\times \left ( \dfrac{1}{4} \right )^{2}$

$I=0\cdot 5\;kgm^{2}$

6. What are the factors on which moment of inertia of a body depends?

Ans.

(i) Mass of the body

(ii) Shape and size of the body

(iii) Position of the axis of rotation

7. Two particles in an iAnsated system undergo head on collision. What is the acceleration of the centre of mass of the system?

Ans. Acceleration of center of mass is zero as all forces are internal forces.

8. Which component of a force does not contribute towards torque?

Ans. The radial component of a force does not contribute towards torque.

9. What is the position of centre of mass of a rectangular lamina?

Ans. The centre of mass of a rectangular lamina is the point of intersection of diagonals.

10. Does the centre of mass of a body necessarily lie inside the body?

Ans. The centre of mass (C.M.) is a point where the mass of a body is supposed to be concentrated. The centre of mass of a body need not necessarily lie within it. For example, the C.M. of bodies such as a ring, a hollow sphere, etc., lies outside the body.

### Section-B (2 Marks Questions)

11. A planet revolves around on massive star in a highly elliptical orbit is its angular momentum constant over the entire orbit. Give reason?

Ans. A planet revolves around the star under the effect of gravitational force since the force is radial and does not contribute towards torque. Thus in the absence of an external torque angular momentum of the planet remains constant.

12. Prove the relation $vec{\tau }=\dfrac{d\vec{L}}{dt}$

Ans. We know $\vec{L}=I\vec{\omega }$

Differentiating wrt. Time

$\dfrac{d\vec{L}}{dt}=\dfrac{d}{dt}\left ( I\vec{\omega } \right )=\dfrac{Id\vec{\omega }}{dt}=1\vec{\alpha }$ …(1)

We know that

$\vec{\tau }=I\vec{\alpha }$ …(2)

From (1) and (2) $\vec{\tau }=\dfrac{d\vec{L}}{dt}$

13. What is the torque of the force $\vec{F}=\hat{2}i-\hat{3}j+\hat{4}k$ acting at the point about the $\vec{r}=\left (\hat{3}i-\hat{2}j+\hat{3}k \right )m$ origin?

Ans. $\vec{\tau }=\vec{r}\times \vec{F}$

$\vec{\tau }=\begin{vmatrix} \hat{}i & \hat{}j & \hat{}k\\ 2 & -3 & 4\\ 3& 2 & 3 \end{vmatrix}$

$\vec{\tau }=\left ( -\hat{17}i+\hat{6}j+\hat{13}k \right )NM$

14. What is the value of linear velocity if $\vec{\omega }=\hat{3}i-\hat{4}j+\hat{}k$ and $\vec{r}=\hat{}5i-\hat{6}j+\hat{6}k$ ?

Ans. $\vec{v}=\vec{\omega }\times \vec{r}$

$\vec{v}=\left ( \hat{3}i-\hat{4}j+\hat{}k \right )\times \left ( \hat{}5i-\hat{6}j+\hat{6}k \right )$

$\vec{t}=\begin{vmatrix} \hat{}i & \hat{}j & \hat{}k\\ 3& -4 & 1\\ 5& -6 & 6 \end{vmatrix}$

$\vec{v}=\left ( -\hat{18}i-\hat{13}j+\hat{2}k \right )m/s$

15. Find the expression for radius of gyration of a Ansid sphere about one of its diameters?

Ans. M.I. of a Ansid sphere about its diameter $=\dfrac{2}{5}MR^{2}$

K = Radius of Gyration

$I=MK^{2}=\dfrac{2}{5}MR^{2}$

$K^{2}=\dfrac{2}{5}R^{2}$

$K=\sqrt{\dfrac{2}{5}}R$

16. Prove that the centre of mass of two particles divides the line joining the particles in the inverse ratio of their masses?

Ans. $\vec{r}_{cm}=\dfrac{m_{1}+\vec{r}_{1}+m_{2}\vec{r}_{2}}{m_{1}+m_{2}}$

If centre of mass is at the origin

$\vec{r}_{cm}=0$

$\Rightarrow m_{1}\vec{r}_{1}+m_{2}\vec{r}_{2}=0$

$m_{1}\vec{r}_{1}=-m_{2}\vec{r}_{2}$

In terms of magnitude $m_{1}\left | \vec{r}_{1} \right |=m_{2}\left | \vec{r}_{2} \right |$

$\Rightarrow \dfrac{m_{1}}{m_{2}}=\dfrac{r_{2}}{r_{1}}$

## PDF Summary - Class 11 Physics System of Particles and Rotational Motion Notes (Chapter 6)

System of particles and rotational motion comes under the fifth unit, Motion of system and particles. This along with Unit IV and Unit VI have a total weightage of 17 marks, which implies students will definitely find questions from this chapter. This is purely an understanding based chapter which talks about the system of particles and rotational motion. The topics extensively covered in the notes of physics class 11 chapter 6 are:

• Centre of mass and its motion.

• Centre of mass of a 2 particle system, rigid body and a uniform rod.

• Momentum of force and momentum conservation.

• Torque.

• Moment of Inertia.

• Angular momentum and laws of conservation of momentum.

• Radius of gyration.

• Parallel and perpendicular axis theorem.

### Notes of System of Particles and Rotational Motion

Given below are the brief explanations of some important concepts and topics covered in the chapter. For an in-depth understanding of the same, refer to notes of system of particles and rotational motion class 11.

• Centre of Mass

The centre of mass of a body is the point at which the entire mass of the body is said to be concentrated at. It is also defined as the balancing point of the system. If any external force is to be applied at the centre of mass, the body is said to remain unaffected. It means that the body will stay in rest if at rest and there will be no change in the velocity of the body in motion.

For the centre of mass of a two particle system at motion,

$\overline{v} = \frac{m_{1}v_{1} + m_{2}v_{2}}{m_{1} + m_{2}}$

$\overline{a} = \frac{m_{1}a_{1} + m_{2}a_{2}}{m_{1} + m_{2}}$

Where,

$\overline{v}$ = Velocity of the centre of mass.

$\overline{a}$ = Acceleration of the centre of mass.

• Torque

The turning effect of force about a fixed axis is defined as Torque. It can also be defined as the Moment of force. The SI unit of Torque is Nm.

$\tau = \overline{r} \times \overline{F} = rF Sin \theta$

Where,

τ = Moment of force or torque

= Perpendicular distance

= Force

θ = Angle between the two vectors r and F

Torque can also be calculated in  the terms of angular moment. The relationship between torque and angular momentum is defined by:

τ = dL/dt

• Moment of Inertia

Moment of Inertia is the phenomenon by which the body in motion opposes the change in its rotational motion. Mathematically, it is defined as the product of mass of particles and their distance from the axis of rotation. It is also called the rotational inertia of the body.

## Importances of Systems of Particles and Rotational Motion Class 11 Notes CBSE Physics Chapter 6 (Free PDF Download)

The availability of free PDF download notes for CBSE Class 11 Physics Chapter 6 - "Systems of Particles and Rotational Motion" holds significant importance for students. This chapter lays the foundation for understanding complex concepts related to rotational dynamics, which are not only crucial for academic success but also have wide-ranging applications in various fields of science and engineering. These notes offer a structured and concise overview, simplifying intricate topics like angular momentum, moment of inertia, and rotational equilibrium. Understanding these principles is vital in comprehending the behavior of objects in motion, from the spinning of celestial bodies to the mechanics of machinery. Accessible notes like these facilitate better exam preparation, foster a deeper understanding of fundamental physics, and pave the way for students to apply these principles in real-world scenarios, making them an indispensable resource for aspiring physicists and engineers.

## Conclusion

Vedatu’s FREE Revision notes PDF download for CBSE Class 11 Physics Chapter 6 - "Systems of Particles and Rotational Motion" is a boon for students. These notes provide a comprehensive and concise resource that simplifies complex concepts in rotational dynamics. Understanding the principles discussed in this chapter is crucial not only for academic success but also for real-world applications in engineering and physics. These notes offer students a structured pathway to grasp topics like angular momentum, moment of inertia, and rotational equilibrium. They not only aid in exam preparation but also empower students to apply these fundamental principles in various scientific and practical scenarios. Overall, these downloadable notes are an invaluable tool for enhancing students' understanding and competence in the realm of rotational motion.

## FAQs on Systems of Particles and Rotational Motion Class 11 Notes CBSE Physics Chapter 6 (Free PDF Download)

1. What do You Understand by Parallel and Perpendicular Axis Theorem?

Ans: Parallel axis theorem states that the moment of inertia of a body is the sum of moment of inertia about a parallel axis passing through the centre of mass and Ma2, where M is the mass of the body and a is the perpendicular distance between the two axes.

Perpendicular axis theorem states that the moment of inertia of a body about a perpendicular axis can be calculated by the sum of the moment of inertias of the body about two axes perpendicular to each other and intersects at the point where the perpendicular axis passes.

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2. Define Angular Momentum?

Ans: Angular momentum is defined as rotational momentum or moment of momentum. It is the rotational equivalent of linear momentum. Conservation of angular momentum states that angular momentum is a conserved quantity, which means that the angular momentum in a closed system remains unchanged. Mathematically,

L = r̅ × p̅

It can also be defined as the product of Moment of Inertia and the angular velocity.

L = Iω

Where,

I = Moment of Inertia

ω = Angular velocity

The SI unit of angular momentum is kgm2/s.

3. How can I download the PDF file of notes of Chapter 6 of Class 11 Physics?

Ans: The steps mentioned below will help you to download the PDF file of notes of Chapter 6 of Class 11 Physics:

• Visit the page Class 11 Physics Revision Notes for Chapter 6.

• This will help you to reach the page of Vedantu.

• As the link will open, the website of Vedantu will appear on your device screen.

• The “Download PDF” option will be available on the page.

• By clicking this option you will get access to download the PDF file.

These notes are available at free of cost and can be accessed from the Vedantu app as well.

4. What are the concepts discussed in Chapter 6 of Class 11 Physics?

Ans: The chapter “System of Particles and Rotational Motion” is a very important and scoring chapter for a student of Class 11. This chapter is very easy to understand. The themes or points mentioned in this chapter are:

• The  motion of Centre of Mass

• Centre of Mass of a uniform rod, rigid body and 2 particle system.

• Momentum Conservation and Momentum of Force

• Torque

• Moment of Inertia

• Laws of Preservation of Angular Momentum and Angular Momentum

• Radius of Gyration

• Perpendicular and Parallel Axis Theorem

5. Note down some differences between the centre of gravity and the centre of mass.

Ans: Centre of Mass – It is defined as the point where the total mass of the body is supposed to be concentrated to describe the motion of the body as a particle. This does not lie in the object's body.

Centre of Gravity – The point where the total weight of the body is presumed to be concentrated, which means that on this point, the resultant gravitational force on all the particles of the body acts. It is always present in the object's body.

6. Write the characteristics of the angular momentum.

Ans: The important features of the angular momentum are:

• With respect to a point, the angular momentum provides an idea regarding the strength of its rotational tendency about that point.

• The definition of angular momentum is in terms of mass, distance from the reference point and particle's velocity i.e. L = mvr.

• It is important to know about the vector concept of angular momentum. With the help of the right-hand rule, the direction of angular momentum can be determined. Velocity and distance are vertical to the direction of angular momentum.

7. What is the moment of inertia of a body rotating about the axis?

Ans: The moment of inertia of a body rotating about the axis is defined as the sum of the product of the square of the distance from the axis and mass of each particle of the body.

This helps to know about the force that the body would take to slow down, speed up or stop.

The factors on which the moment of inertia of a body rotating about the axis depends on:

• Body’s distance from the axis.

• Mass distribution of the body.