NCERT Books for Class 11 Physics Chapter 7 - Systems of Particles and Rotational Motion - Free PDF Download
FAQs on NCERT Books Free Download for Class 11 Physics Chapter 7 - Systems of Particles and Rotational Motion
1. What are the most frequently asked 5-mark questions from Chapter 7, Systems of Particles and Rotational Motion, for the CBSE Class 11 exams?
For the Class 11 Physics exam, some of the most important 5-mark questions from this chapter involve comprehensive derivations and applications. According to the 2025-26 board trends, you should focus on:
- Stating and proving the theorem of parallel axes and the theorem of perpendicular axes for moment of inertia, followed by a numerical application.
- Deriving the expression for the kinetic energy of a body in pure rolling motion and explaining the distribution between translational and rotational kinetic energy.
- Explaining the principle of conservation of angular momentum with a suitable example and deriving the relation between torque and angular momentum (τ = dL/dt).
2. Which derivations are considered important for the exam from the Rotational Motion chapter?
From an examination perspective, several derivations in this chapter are crucial. Key derivations often asked in exams include:
- The expression for the moment of inertia of a thin circular ring and a solid disc about an axis passing through their centre and perpendicular to their plane.
- The relationship between torque (τ) and angular acceleration (α), which is τ = Iα.
- The derivation for the acceleration of a body rolling down a smooth inclined plane without slipping.
- The vector relationship between angular momentum (L) and linear momentum (p), L = r × p.
3. How can the theorems of parallel and perpendicular axes be applied to solve complex problems, and why are they so important?
These theorems are vital because they provide a shortcut to find the moment of inertia of a body about an axis without performing complex integration every time. The Parallel Axis Theorem is used to find the moment of inertia about any axis parallel to an axis passing through the centre of mass. The Perpendicular Axis Theorem (for planar bodies) relates the moment of inertia about an axis perpendicular to the plane to the moments of inertia about two axes in the plane. They are important because they allow you to calculate the moment of inertia for complex configurations, such as finding the MI of a disc about its tangent or a rod about one of its ends.
4. What types of numerical problems based on Torque and Moment of Inertia are expected in the exam?
For the Class 11 exam, you can expect numericals that test your understanding of these core concepts. Important types include:
- Calculating the net torque on a body when multiple forces are applied at different points.
- Finding the moment of inertia of a system of discrete particles or simple composite rigid bodies.
- Problems combining torque and moment of inertia to find the angular acceleration (using τ = Iα).
- Questions on the equilibrium of a rigid body, where you must ensure that both the net force and net torque are zero.
5. What is the conceptual difference between Centre of Mass and Centre of Gravity, and in what situations can they be considered the same?
The Centre of Mass (CoM) is a point representing the mean position of the matter in a body. It depends only on the distribution of mass. The Centre of Gravity (CoG) is the point through which the total gravitational force (weight) on the body acts. The key difference is that CoG depends on the gravitational field. They can be considered the same only when the gravitational field is uniform and parallel across the entire body. For most objects on Earth, this is a valid assumption. However, for extremely large objects, like a mountain, the CoM and CoG may be at slightly different positions.
6. Which topics from Rotational Motion are crucial for answering 2-mark and 3-mark questions?
For short-answer questions (2 and 3 marks), a clear understanding of fundamental concepts is key. Important topics include:
- Definitions of angular velocity, angular acceleration, torque, and moment of inertia.
- The relation between linear velocity and angular velocity (v = ω × r).
- The conditions for static and dynamic equilibrium of a rigid body.
- Stating the principle of conservation of angular momentum and providing one practical example.
- Calculating the radius of gyration for simple bodies.
7. Why is the conservation of angular momentum a fundamental principle in physics? Provide a real-world example where it is applied.
The conservation of angular momentum is a fundamental principle because it arises from the rotational symmetry of physical space—meaning, the laws of physics are the same regardless of orientation. The principle states that if no external torque acts on a system, its total angular momentum remains constant. A classic real-world example is an ice skater performing a spin. When the skater pulls their arms inward, their moment of inertia (I) decreases. To conserve angular momentum (L = Iω), their angular velocity (ω) must increase, causing them to spin faster.
8. What are some important questions related to the kinematics of rolling motion without slipping?
Rolling motion is a frequently tested topic. Important questions often involve:
- Deriving the condition for pure rolling, which is v_cm = Rω, where v_cm is the velocity of the centre of mass.
- Calculating the total kinetic energy of a rolling body, which is the sum of its translational (1/2 mv²) and rotational (1/2 Iω²) kinetic energies.
- Solving problems to find the acceleration of a solid sphere, cylinder, or ring rolling down an inclined plane.
9. How does the concept of a vector product (cross product) form the basis for defining rotational quantities like torque and angular momentum?
The vector product is essential because rotational effects depend on both the magnitude of a force (or momentum) and the perpendicular distance from the axis of rotation. The cross product mathematically captures this relationship. Torque (τ = r × F) and angular momentum (L = r × p) are defined as cross products because:
- Their magnitude depends on the sine of the angle between the position vector (r) and the force/momentum vector, which isolates the perpendicular component.
- Their direction is correctly given as perpendicular to the plane of rotation, following the right-hand rule.
