Did you ever observe how a bicycle wheel spinning round and round gradually comes to a stop when you stop pedalling? This basic observation illustrates concepts of rotational motion and moment of inertia, the important concepts developed in Class 11 Physics Chapter 6 - System of Particles and Rotational Motion. This chapter is more than formulas; it creates a solid conceptual background of the behaviour of rotating bodies in mechanics, engineering, and daily life.
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The chapter addresses the fundamentals of centre of mass, torque, angular momentum, equilibrium of rigid bodies, and the theory of the detailed analysis of rotational motion. These are the concepts that lie behind a higher level of physics and are particularly vital to a student who is going to undertake CBSE board exams, JEE, NEET, and other efficient entrance exams. The subject experts in the NCERT Class 11 Physics Chapter 6 Notes System of Particles and Rotational Motion have made it easier to understand complicated concepts by short descriptions of significant theories, derivations and formulas, improved visualisation using labelled diagrams, problems and solved examples. These well-made Class 11 Physics NCERT Notes will enable students to tighten their core foundations, revise, and acquire the confidence to handle questions at exam and competition levels comfortably.
Also, students can refer,
Learn these concepts of centre of mass, torque, angular momentum, and rotational dynamics using our simple-to-understand NCERT Class 11 Physics Chapter 6 Notes. The free PDF is very explanatory in nature, with the essential formulas and example answers that may be used in CBSE board exams as well as competitive exams such as JEE and NEET.
Chapter 6 of Physics in NCERT Class 11 on System of Particles and Rotational Motion provides a compact and organised overview of important concepts such as the torque, angular momentum, and moment of inertia. These notes can be used to revise within a very short time and prepare for exams in CBSE, JEE, and NEET.
(Here m1 & m2 are two bodies in which m1 is at a distance x1, & m2 at a distance x2 from the origin O).
The total contribution of each such integral and the integral x dm is zero. Therefore, the COM coincides with its geometric centre.
The centre of mass coincides with the geometric centre, and with the same geometry is applicable to homogenous rings, discs, spheres, or even thick rods of circular or rectangular cross-sections;
Differentiating w.r.t. time, we get,
Again, differentiating w.r.t. time, we get,
M
Instead of considering extended bodies as single particles, we can consider them as systems of particles.
Where
In case when the total external force acting on a system of particles is zero (
(
The Centre of mass having velocity also remains constant (Since
If the total external force on a body is zero, then the internal forces cause complex trajectories of individual particles in spite of the COM moving with a constant velocity.
The translational state of the motion of the rigid body is due to the changes in force, i.e. its total linear momentum changes.
The rotational state of motion of the rigid body is due to the changes in torque, i.e. the total angular momentum of the body changes.
Unless stated otherwise, only external forces and torques should be dealt.
Total force zero = Translational Equilibrium
Total torque zero = Rotational Equilibrium
I = Mk2, where k is the radius of gyration.
We can derive equations of motion similar to translational motion.
Translational motion
v=vo+at
x=xo+vot+0.5at2
v2=vo2+2as
Rotational Motion
ω=ωo+αt
θ=θo+ωot+0.5αt2
ω2=ωo2+2αθ
Q1: The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it?
a) the forces may be acting radially from a point on the axis
b) the forces may be acting on the axis of rotation
c) the forces may be acting parallel to the axis of rotation
d) the torque caused by some forces may be equal and opposite to that caused by other forces
Answer:
Torque is given by
Or
1. When the force is acting radially in the direction of
$\tau=r F \sin 0^{\circ}=0$
2. When the forces are acting on the axis of rotation then
3. The component of forces in the plane of
4. When torques are equal in magnitude but opposite in direction, the net resultant is 0.
Hence, the answers are options (a) and (b).
Q2: A Merry-go-round, made of a ring-like platform of radius
Answer:
As no external torque acts on the system, angular momentum should be conserved.
Hence.
where
velocity of the system.
From Eq. (i),
(where
(As mass is reduced to half, hence moment of inertia is also reduced to half)
Q3: Which of the following points A, B and C is the likely position of the centre of mass of the system shown in Fig. 7.1?
Answer:
The volume of the hollow sphere is occupied equally by the air and sand. Since the pressure exerted by the air region is less than that of sand, the mass of sand is greater than the air. The centre of mass shifts towards a heavier portion, which in this case is sand. B is exactly at the line dividing air and sand, so it is incorrect. D is at the farthest end and divides the sand area very unequally, so it also cancels out. C is almost at the centre with regard to the mass.
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NCERT Class 11 Notes Chapter-Wise contain brief, clearly organized and simple summaries of every chapter. These are notes on major concepts, formulas, derivations and diagrams as per the newest CBSE syllabus that enable students to revise quickly. They are of great utility in board exams and also in competitive exams as JEE and NEET.
Frequently Asked Questions (FAQs)
Rotational motion principles are used in:
This chapter is a scoring topic in JEE, NEET, and CBSE board exams. It helps in solving complex physics problems involving motion, forces, and energy conservation.
Rolling motion is a combination of translational and rotational motion.
Pure rolling occurs when there is no slipping, and v = Rω (where v is linear velocity, R is radius, and ω is angular velocity).
If no external torque acts on a system, angular momentum (L = Iω) remains constant. This principle explains why a skater spins faster when pulling in their arms.
The moment of inertia (I) is the rotational equivalent of mass. It represents an object's resistance to angular acceleration and depends on mass distribution.
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