# System of Particles and Rotational Motion Notes | SwaVid

System of Particles and Rotational Motion, NCERT Class 11 Physics: notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers.

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# System of Particles and Rotational Motion

## Formulas and definitions

## Key ideas

## Common mistakes

## Quick checks

## Keep going

## Questions parents ask

## Class 11 Physics on SwaVid

### Centre of mass

### Vector product of two vectors

### Angular velocity and acceleration

### Torque and angular momentum

### Equilibrium of a rigid body

### Moment of inertia

### Kinematics and dynamics of rotation

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SwaVid › CBSE › Class 11 › Physics › System of Particles and Rotational Motion

Notes written by SwaVid from the NCERT textbook.

Class 11 Physics, Chapter 6. Key ideas, formulas and common mistakes.

CBSE prints 17 marks for Units IV-VI together, not for this chapter alone.

Short answer. This chapter explains the motion of extended bodies and systems of particles using centre of mass and rotational dynamics. It establishes rotational analogues of linear motion quantities such as torque, angular momentum, and moment of inertia.

Source: NCERT Physics Part I (Reprint 2026-27) , Chapter 6, System of Particles and Rotational Motion

The centre of mass of a system of particles is a point that moves as if all the mass of the system were concentrated there and all external forces were applied at that point. Internal forces cancel out in pairs due to Newton's third law and do not affect its acceleration.

The vector product or cross product of two vectors A and B produces a vector C = A × B with magnitude |A||B| sin θ. Its direction is perpendicular to the plane containing A and B, given by the right-hand screw rule.

Every particle of a rigid body rotating about a fixed axis moves in a circle with the same angular velocity ω. The linear velocity of a particle at perpendicular distance r from the axis has magnitude v = ω r, and the vector relation is v = ω × r.

Torque is the rotational analogue of force and is defined as τ = r × F. Angular momentum is defined as l = r × p, and its rate of change with time equals the net external torque acting on the system.

A rigid body is in mechanical equilibrium when both translational and rotational equilibrium conditions are satisfied. This requires that the vector sum of all external forces is zero and the vector sum of all external torques is zero.

Moment of inertia measures the rotational inertia of a body about a given axis and depends on the mass distribution relative to that axis. For a system of particles, it is given by I = ∑ mᵢ rᵢ².

Rotational motion about a fixed axis follows equations analogous to linear motion under constant acceleration. Work done by a constant torque is τ θ, rotational kinetic energy is (1/2) I ω², and the equation of motion is τ = I α.

Try each question first. Then tap it to see the answer.

X = (m₁ x₁ + m₂ x₂) / (m₁ + m₂)

X = (1.0 × 0 + 3.0 × 2.0) / (1.0 + 3.0)

X = 6.0 / 4.0 = 1.5 m

1.5 m

τ = r F sin θ

Here θ = 90°, so sin θ = 1

τ = 0.25 × 10 × 1 = 2.5 N m

2.5 N m

K = (1/2) I ω²

K = 0.5 × 4.0 × (5.0)²

K = 2.0 × 25.0 = 50 J

50 J

Gravitation .

Laws of Motion .

Work, Energy and Power .

The 14 chapters of Class 11 Physics .

CBSE does not give marks to one chapter. It prints 17 marks for Units IV-VI together (Work, Energy and Power; System of Particles and Rigid Body; Gravitation). System of Particles and Rotational Motion is part of that group.

No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed.

Gravitation.

SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works.

- Ch 6 NCERT book
- 17 marks, Units IV-VI together
- 3 quick checks
- Treating moment of inertia as a fixed scalar property of a body independent of the axis . Always specify the axis of rotation. The same object has different moments of inertia about different axes because the perpendicular distances of its mass elements change.
- Using F × r instead of r × F for torque . The cross product is anti-commutative, so F × r = -(r × F). Always write torque as r × F, where r is the position vector from the reference point to the line of action of force.
- Assuming centre of gravity is always identical to centre of mass . The centre of gravity coincides with the centre of mass only in a uniform gravitational field. In non-uniform fields, they can be at different points.
- Forgetting that internal forces do not change the total angular momentum of a system . By Newton's third law, internal torques sum to zero when forces act along the lines joining particle pairs. Only net external torque changes total angular momentum.

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