NCERT · Class XI · Chapter 6

System of Particles & Rotational Motion
— True/False Master Drill —

Test every subtle idea from centre of mass to rolling motion using high‑yield True/False statements before you jump into full‑length numericals.

⏱15–20 min concept check
🎯24+ carefully curated T/F statements
📚NCERT Ch‑6 · Boards · JEE/NEET
Start True/False Quiz ➜ Jump to Detailed Notes
Quick Chapter Snapshot
At a Glance
Core Ideas
COM, Torque, I, L
Centre of mass, turning effect, rotational inertia & angular momentum.
Exam Weightage
~12–15%
Across Mechanics questions in Boards, JEE & NEET.
Typical Questions
Concept + Numericals
True/False, reasoning & mixed rolling problems.
Why This Chapter Matters
Entrance Exams
  • 🧠
    Foundation for Rotation & Rigid Bodies Concepts of COM, torque, moment of inertia and angular momentum reappear in advanced Mechanics, SHM and Rotational Dynamics questions.
  • 📈
    High-Yield for JEE/NEET Standard patterns include pure rotation, rolling without slipping, conservation of angular momentum and comparison of kinetic energies.
  • 🌍
    Real-World Intuition Explains why doors open easier at the handle, why skaters spin faster when they fold arms, and how wheels roll without slipping.
Key Concept Highlights
COM · Torque · Rolling
System of Particles & COM Treats a whole system as if all mass were concentrated at one point whose motion responds only to external forces.
Rigid Body & Pure Translation In pure translation, every point of a rigid body has the same velocity at an instant, with no rotation about any axis.
Torque & Rotational Dynamics Torque is the turning effect of a force and produces angular acceleration according to τ = Iα about a chosen axis.
Moment of Inertia Measures rotational inertia and depends on both mass and how far it is distributed from the axis of rotation.
Angular Momentum & Conservation For zero external torque, total angular momentum of a system remains constant even if the body changes its shape.
Rolling Without Slipping A combination of translation and rotation where the contact point is instantaneously at rest and v = ωR for the centre of mass.
Important Formula Capsules
Revise in 60s
Centre of Mass
\( \vec{R}_{\text{CM}} = \dfrac{\sum_i m_i \vec{r}_i}{\sum_i m_i} \)
Linear Momentum & COM
\( \vec{P} = M \vec{V}_{\text{CM}} \)
Torque & Rotation
\( \vec{\tau} = \vec{r} \times \vec{F}, \quad \tau = I \alpha \)
Moment of Inertia
\( I = \sum_i m_i r_i^2 \)
Angular Momentum
\( \vec{L} = \vec{r} \times \vec{p}, \quad L = I \omega \)
Rotational KE & Rolling
\( K_{\text{rot}} = \dfrac{1}{2} I \omega^2, \quad v = \omega R \)
What You Will Learn
True/False Focus
  • ①
    Judge whether statements about centre of mass location, motion and dependence on external forces are logically correct.
  • ②
    Distinguish between linear and rotational analogues: force vs torque, mass vs moment of inertia, momentum vs angular momentum.
  • ③
    Spot hidden traps in statements about equilibrium, net force, net torque and conservation laws.
  • ④
    Analyse rolling without slipping, kinetic energy distribution and instantaneous axis of rotation using crisp True/False logic.
  • ⑤
    Apply parallel and perpendicular axis theorems mentally to reason about how moment of inertia changes with geometry.
Navigation · Detailed Notes
Quick Links
Notes: Centre of Mass Notes: Torque & L Notes: Moment of Inertia Notes: Rolling Motion Go to True/False Set
Exam Strategy & T/F Analytics
Boards · JEE · NEET
Strategy Playbook
  • Step 1 · Concept Isolation
    First, review NCERT definitions of COM, torque, rigid body, pure translation/rotation and rolling so that every True/False feels “obvious”.
  • Step 2 · Think in Analogies
    Map force→torque, mass→moment of inertia, linear momentum→angular momentum and straight‑line motion→rotation in each statement before deciding its truth value.
  • Step 3 · Conservation Filters
    Ask “Is any external force/torque present?” to quickly accept or reject claims about conservation of momentum or angular momentum.
  • Step 4 · Rolling Intuition
    Remember: in pure rolling without slipping, contact point is instantaneously at rest, COM obeys v = ωR and KE is split into translational + rotational parts.
  • Step 5 · Time-Bound Drills
    Solve the full True/False set in one go under a timer, then revisit each incorrect statement with a quick sketch or free‑body diagram.
True/False Analytics
Statements Covered: COM, equilibrium, torque, I, rolling, angular momentum, explosions & energy.
Centre of Mass & Motion Torque vs Force Moment of Inertia & Shape Angular Momentum & Conservation Rolling Without Slipping Explosions & COM Path Rigid Body Dynamics
Your Progress 0 / 25 attempted
Q 01 / 25
The centre of mass of a system of particles always lies on one of the particles.
Q 02 / 25
For a system of particles with no external force, the velocity of centre of mass remains constant.
Q 03 / 25
In pure translation of a rigid body, all particles have the same velocity at any instant.
Q 04 / 25
The position of the centre of mass of a uniform rod is always at its geometrical centre.
Q 05 / 25
Torque is a scalar quantity because it is the product of force and perpendicular distance.
Q 06 / 25
A rigid body under the action of several forces can be in translational equilibrium even if the net torque is not zero.
Q 07 / 25
A body can have zero net force and still have non-zero angular acceleration about some point.
Q 08 / 25
The moment of inertia of a body depends only on its total mass, not on how that mass is distributed.
Q 09 / 25
For a given rigid body and axis, the moment of inertia remains constant even if its angular velocity changes.
Q 10 / 25
The SI unit of moment of inertia is kg m2^{2}2.
Q 11 / 25
For a symmetric rigid body, the centre of mass and the geometric centre always coincide, irrespective of mass distribution.
Q 12 / 25
The angular momentum of a particle about a point depends on the choice of that point.
Q 13 / 25
If no external torque acts on a system, its angular momentum about any fixed point must be zero.
Q 14 / 25
In pure rolling without slipping on a horizontal surface, the velocity of the point of contact with the ground is zero relative to the ground.
Q 15 / 25
In pure rolling without slipping, translational kinetic energy is always greater than rotational kinetic energy for any rigid body.
Q 16 / 25
For a rigid body rotating about a fixed axis, all points of the body have the same angular velocity but different linear speeds.
Q 17 / 25
For any rigid body rotating about a fixed axis, angular momentum is always parallel to angular velocity.
Q 18 / 25
The parallel axis theorem allows calculation of moment of inertia about any axis parallel to one through the centre of mass.
Q 19 / 25
The perpendicular axis theorem is applicable to any three-dimensional rigid body.
Q 20 / 25
If a spinning skater pulls in his arms, his angular velocity increases because his internal forces produce a net external torque.
Q 21 / 25
For a uniform disc and a uniform ring of the same mass and radius rolling without slipping with the same linear speed, the ring has greater total kinetic energy.
Q 22 / 25
For a rigid body rolling without slipping down an incline, a larger moment of inertia (for fixed mass and radius) leads to a larger linear acceleration of the centre of mass.
Q 23 / 25
In a central explosion of a projectile in flight (no external forces other than gravity), the centre of mass of all fragments continues to follow the same parabolic trajectory as the original projectile.
Q 24 / 25
A force whose line of action passes through the centre of mass of a rigid body can never change the body’s rotational state about any axis.
Q 25 / 25
For a rigid body rotating freely in space with no external torque, its rotational kinetic energy must remain constant even if the axis about which it spins in space changes.
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