Introduction to System of Particles and Rotational Motion

The chapter System of Particles and Rotational Motion extends classical mechanics to multiple particle systems and rotating bodies. NEET Physics often includes questions on torque, moment of inertia, angular momentum, and rotational kinetic energy, making this chapter essential for aspirants.

StudentBro notes provide detailed explanations, diagrams, and problem-solving methods tailored to the NEET exam.

Direct Links to Download 2025-26 Physics Notes (PDF)

► Click “Download Here” next to your subject to access the free PDF.

Centre of Mass (CM)

• The centre of mass of a system of particles is the point at which the entire mass of the system can be considered to be concentrated.

• For a system of particles: R_cm = (Σ m_i r_i) / (Σ m_i)

• Motion of the system can be studied by considering the motion of the centre of mass.

NEET problems often involve centre of mass of two or more bodies, uniform rod, and continuous systems.

Linear Momentum of a System of Particles

• The total linear momentum of a system is the sum of the linear momenta of all particles: P = Σ m_i v_i

• The motion of the centre of mass obeys Newton’s Second Law: F_ext = M_total × a_cm

• Useful for solving NEET questions on collisions, rockets, and system dynamics.

StudentBro notes provide clarity on applying momentum concepts to multiple particle systems.

Torque and Moment of Force

• Torque (or moment of force) is the rotational equivalent of force:
  τ = r × F

  • r = position vector

  • F = applied force

• Torque determines angular acceleration of a rigid body: τ = I α, where I is moment of inertia.

• NEET often tests torque in levers, pulleys, and rotational equilibrium.

Understanding torque is crucial for rotational dynamics problems in NEET.

Moment of Inertia (MI)

• Moment of inertia measures the resistance of a body to rotational motion.

• Formula for discrete particles: I = Σ m_i r_i²

• Formula for continuous bodies: I = ∫ r² dm

• Important NEET applications: Rods, disks, spheres, cylinders, and hollow bodies.

StudentBro notes explain MI concepts with tables of standard bodies and parallel/perpendicular axis theorems.

Parallel and Perpendicular Axis Theorems

• Parallel Axis Theorem: I = I_cm + Md²

• Perpendicular Axis Theorem: I_z = I_x + I_y (for planar bodies)

• Useful for calculating MI of composite bodies in NEET numerical problems.

Rotational Kinematics

Rotational motion equations are analogous to linear motion:

• θ = angular displacement

• ω = angular velocity

• α = angular acceleration

Equations:

• ω = ω_0 + αt

• θ = ω_0 t + ½ α t²

• ω² = ω_0² + 2αθ

NEET questions often require converting linear quantities to angular equivalents.

Rotational Kinetic Energy

• Rotating bodies possess kinetic energy due to rotation:
  KE_rot = ½ I ω²

• For rolling objects, total kinetic energy:
  KE_total = KE_translational + KE_rotational = ½ Mv² + ½ Iω²

• Important for NEET questions involving rolling motion of cylinders and spheres.

StudentBro notes provide clear step-by-step derivations for NEET aspirants.

Angular Momentum

• Angular momentum is the rotational equivalent of linear momentum:
  L = I ω

• Law of conservation of angular momentum: In absence of external torque, L = constant

• Applications: Spinning ice skaters, planets, and rotational collisions

NEET frequently tests angular momentum in practical and theoretical problems.

Torque and Rotational Dynamics

• Newton’s Second Law for rotation: τ_net = I α

• Rotational analogues: Force → Torque, Mass → Moment of Inertia, Linear Acceleration → Angular Acceleration

• NEET numerical problems often involve calculating torque, angular acceleration, and angular displacement.

Rolling Motion

• Rolling combines translation and rotation: v = Rω

• Friction is necessary for rolling without slipping

• Total kinetic energy: KE_total = ½ Mv² + ½ Iω²

• NEET problems include spheres, cylinders, and disks rolling down an incline.

StudentBro notes emphasize solving rolling motion problems efficiently.

Equilibrium of a Rigid Body

• A rigid body is in equilibrium if:

  • Σ F = 0 (translational equilibrium)

  • Σ τ = 0 (rotational equilibrium)

• Useful in solving NEET problems on levers, beams, and pulleys.

Applications in NEET

• Motion of rigid bodies on inclined planes

• Rolling objects and rotational energy problems

• Torque and angular acceleration in levers and pulleys

• Conservation of angular momentum in rotating systems

Mastery of this chapter ensures confident problem-solving in both theory and numericals for NEET.

Tips for NEET Preparation on System of Particles and Rotational Motion

1. Memorize formulas for MI of standard shapes.

2. Practice translating linear motion formulas into rotational analogues.

3. Solve torque and angular momentum numerical problems regularly.

4. Understand rolling motion with and without slipping.

5. Draw diagrams for all rigid body and system of particles questions.

StudentBro notes provide exam-oriented guidance for applying these tips effectively.

Advantages of StudentBro NEET Physics Notes

• Covers centre of mass, torque, MI, angular momentum, rotational KE, and rolling motion

• Step-by-step examples and diagrams included

• Structured for easy revision and conceptual clarity

• Focused on NEET syllabus and high-yield problems

These notes ensure aspirants can confidently tackle system of particles and rotational motion questions.

Conclusion

The chapter System of Particles and Rotational Motion is critical for NEET Physics. Mastery of centre of mass, moment of inertia, torque, angular momentum, and rotational energy is essential for solving conceptual and numerical problems.

StudentBro NEET Physics notes provide clear, structured, and exam-focused guidance, enabling aspirants to confidently solve rotational dynamics problems and achieve high scores in NEET exams.