Systems of Particles and Rotational Motion is a core and high-weightage chapter in Class 11 Physics that extends the concepts of mechanics from single particles to rigid bodies and systems. This chapter covers important topics such as centre of mass, momentum of a system of particles, torque, angular momentum, rotational kinematics, moment of inertia, radius of gyration, rolling motion, and conservation laws, which are essential for Class 11 exams and competitive exams like JEE and NEET.
NCERT Solutions for Class 11 Physics Chapter 6 – Systems of Particles and Rotational Motion are prepared strictly according to the latest CBSE syllabus and exam pattern. The solutions are written in simple, step-by-step language with clear derivations, diagrams, and solved numericals, helping students build strong conceptual understanding and problem-solving skills.
NCERT Solutions For Class 11 Physics Chapter 6 Systems of Particles and Rotational Motion
Q.
(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be 2MR2/5, where M is the mass of the sphere and R is the radius of the sphere.
(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be MR2/4, find its moment of inertia about an axis normal to the disc and passing through a point on its edge.
Q.
As shown in Fig.7.40, the two sides of a step ladder BA and CA are 1.6 m long and hinged at A. A rope DE, 0.5 m is tied half way up. A weight 40 kg is suspended from a point F, 1.2 m from B along the ladder BA. Assuming the floor to be frictionless and neglecting the weight of the ladder, find the tension in the rope and forces exerted by the floor on the ladder. (Take g = 9.8 ms-2)(Hint: Consider the equilibrium of each side of the ladder separately.)
Q.
A solid disc and a ring, both of radius 10 cm are placed on a horizontal table simultaneously, with initial angular speed equal to 10 π rad s-1. Which of the two will start to roll earlier? The co-efficient of kinetic friction is μk = 0.2.
Q.
A disc rotating about its axis with angular speed ω
o is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is R. What are the linear velocities of the points A, B and C on the disc shown in Fig. 7.41? Will the disc roll in the direction indicated?
Q.
Q.
(a) Prove the theorem of perpendicular axes. (Hint: Square of the distance of a point (x, y) in the x–y plane from an axis through the origin perpendicular to the plane is x2 + y2).
(b) Prove the theorem of parallel axes. (Hint: If the centre of mass is chosen to be the origin).
Q.
Two discs of moments of inertia I1 and I2 about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds ω1 and ω2 are brought into contact face to face with their axes of rotation coincident.
(a) What is the angular speed of the two-disc system?
(b) Show that the kinetic energy of the combined system is less than the sum of the initial kinetic energies of the two discs. How do you account for this loss in energy? Take ω1 ≠ ω2.
Q.
A bullet of mass 10 g and speed 500 ms-1 is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it.. (Hint: The moment of inertia of the door about the vertical axis at one end is ML2/3.)
Q.
A man stands on a rotating platform, with his arms stretched horizontally holding a 5 kg weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then brings his arms close to his body with the distance of each weight from the axis changing from 90 cm to 20cm. The moment of inertia of the man together with the platform may be taken to be constant and equal to 7.6 kg m2.
(a) What is his new angular speed? (Neglect friction.)
(b) Is kinetic energy conserved in the process? If not, from where does the change come about?
Q.
A solid cylinder rolls up an inclined plane of angle of inclination 30°. At the bottom of the inclined plane the centre of mass of the cylinder has a speed of 5 m/s.
(a) How far will the cylinder go up the plane?
(b) How long will it take to return to the bottom?
Q.
Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is
free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?
Q.
The oxygen molecule has a mass of 5.30 × 10–26 kg and a moment of inertia of 1.94×10–46 kg m2 about an axis through its centre perpendicular to the lines joining the two atoms.
Suppose the mean speed of such a molecule in a gas is 500 ms-1 and that its kinetic energy of rotation is two thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.
Q.
A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it?
Q.
A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination.
(a) Will it reach the bottom with the same speed in each case?
(b) Will it take longer to roll down one plane than the other?
(c) If so, which one and why?
Q.
A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5 g are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm. What is the mass of the metre stick?
Q.
From a uniform disk of radius R, a circular hole of radius R/2 is cut out. The centre of the hole is at R/2 from the centre of the original disc. Locate the centre of gravity of the resulting flat body.
Q.
A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope? Assume that there is no slipping.
Q.
(a) A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value? Assume that the turntable rotates without friction.
(b) Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?
Q.
A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s–1. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder?
What is the magnitude of angular momentum of the cylinder about its axis?
Q.
NCERT Solutions For Class 11 Physics Chapter 6 Systems of Particles and Rotational Motion
Q1. What is the centre of mass of a system?
Answer:
The centre of mass of a system is a point where the entire mass of the system can be assumed to be concentrated for studying translational motion.
Q2. Define linear momentum of a system of particles.
Answer:
The linear momentum of a system of particles is the vector sum of the momenta of all individual particles in the system.
Q3. State the law of conservation of linear momentum.
Answer:
If no external force acts on a system, the total linear momentum of the system remains constant.
Q4. What is torque? Write its SI unit.
Answer:
Torque is the turning effect of a force about a point or axis.
SI unit of torque is newton-metre (N m).
Q5. Define angular momentum. Write its expression.
Answer:
Angular momentum is the moment of linear momentum of a particle about a point.
Angular momentum = r × p.
Q6. State the law of conservation of angular momentum.
Answer:
If the net external torque acting on a system is zero, the total angular momentum of the system remains constant.
Q7. What is moment of inertia? On what factors does it depend?
Answer:
Moment of inertia is the rotational analogue of mass and measures resistance to rotational motion.
It depends on the mass of the body, distribution of mass, shape, size, and axis of rotation.
Q8. Write the SI unit and dimensional formula of moment of inertia.
Answer:
SI unit: kg m²
Dimensional formula: [M L²]
Q9. State and explain the parallel axis theorem.
Answer:
The parallel axis theorem states that the moment of inertia about any axis parallel to a given axis is equal to the moment of inertia about the given axis plus mass times the square of the distance between the two axes.
Q10. State the perpendicular axis theorem.
Answer:
For a planar body, the moment of inertia about an axis perpendicular to the plane is equal to the sum of moments of inertia about two mutually perpendicular axes lying in the plane.
Q11. What is rotational kinetic energy?
Answer:
Rotational kinetic energy is the energy possessed by a rotating body due to its rotational motion.
It is given by ½Iω².
Q12. Define angular acceleration.
Answer:
Angular acceleration is the rate of change of angular velocity with respect to time.
Q13. Write the relation between linear velocity and angular velocity.
Answer:
Linear velocity = rω, where r is the radius and ω is the angular velocity.
Q14. What is rolling motion?
Answer:
Rolling motion is a combination of translational motion and rotational motion, where a body rolls without slipping.
Q15. Explain the condition for pure rolling.
Answer:
For pure rolling, the velocity of the point of contact with the ground must be zero relative to the ground.
Q16. Why do dancers pull their arms inward while spinning?
Answer:
By pulling their arms inward, dancers reduce their moment of inertia. Due to conservation of angular momentum, their angular velocity increases.
Q17. What is equilibrium of a rigid body?
Answer:
A rigid body is in equilibrium when both the net external force and net external torque acting on it are zero.
Q18. Distinguish between translational and rotational motion.
Answer:
In translational motion, all particles move with the same velocity.
In rotational motion, particles move in circles about a fixed axis.
Q19. Write two applications of conservation of angular momentum.
Answer:
Ice skaters spinning faster by pulling arms inward.
Rotation of planets around the Sun.
Q20. What is the physical significance of moment of inertia?
Answer:
Moment of inertia determines how difficult it is to change the rotational motion of a body.
FAQs: Class 11 Physics Chapter 6 – Systems of Particles and Rotational Motion
Q1. Is this chapter important for exams?
Yes, it is a high-weightage and foundational mechanics chapter.
Q2. Which topics are most important here?
Centre of mass, torque, moment of inertia, and angular momentum.
Q3. Are numericals asked from this chapter?
Yes, rotational motion and rolling-based numericals are very common.
Q4. Are derivations important in this chapter?
Yes, derivations related to moment of inertia and angular momentum are frequently asked.
Q5. How do NCERT Solutions help?
They provide NCERT-aligned, exam-ready explanations with solved numericals and diagrams.