Class 11 · Chapter 6
Centre of Mass & Collisions
Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.
Centre of Mass & Collisions Overview
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Introduction to Centre of Mass & Collisions
Centre of Mass & Collisions shifts focus from single particles to systems of multiple bodies — locating a system's centre of mass, understanding how it moves under external forces regardless of internal interactions, and analyzing elastic and inelastic collisions using momentum, and for elastic collisions, energy conservation. The prerequisites are Laws of Motion, for momentum, and Work-Energy-Power, for the energy side of elastic collisions. The most common mistake is forgetting that momentum conservation applies to the system as a whole, not to each object individually — students sometimes try to apply Newton's laws to each colliding body separately, accounting for the complicated internal forces during the collision, when momentum conservation elegantly sidesteps that entire problem. A clean way to avoid errors is to clearly separate the two collision types in your head: elastic collisions conserve both momentum and kinetic energy, while inelastic collisions conserve only momentum. Mixing these up is the single most common error on collision problems, and it's entirely avoidable with a moment's check before writing any equations.
This chapter is a direct bridge between the single-particle mechanics of earlier chapters and the rigid-body mechanics of Rotational Motion that follows, and collision problems — especially 1D elastic/inelastic collisions and the coefficient of restitution — are a particularly reliable source of direct, formula-based NEET and JEE questions.
How to Study Centre of Mass & Collisions
Prerequisites
Laws of Motion (for momentum) · Work-Energy-Power (for kinetic energy in elastic collisions)
Recommended approach
Study centre of mass (location and motion) first, then momentum conservation, then elastic and inelastic collisions last, since collisions are really just momentum conservation applied to a specific scenario.
Common mistakes
- Applying Newton's laws to each colliding body separately instead of using system-wide momentum conservation.
- Assuming kinetic energy is conserved in every collision, rather than only in elastic ones.
- Forgetting the extra vector-decomposition step required for 2D (oblique) collisions, and treating them like 1D problems.
Revision strategy
Revise by re-deriving the standard 1D elastic collision velocity formulas from the two conservation equations (momentum and kinetic energy), rather than memorizing the final result.
PYQ strategy
Centre-of-mass-of-a-system-with-a-removed-part PYQs, like a disc with a hole cut out, are a recurring, somewhat trick-based pattern worth specifically practicing.
DPP strategy
Use DPPs on 2D (oblique) collisions specifically — 1D collisions are usually well-practiced by this point, but 2D problems require an extra vector-decomposition step that catches many students off guard.
Exam weightage
Consistently tested in both NEET and JEE; 1D collision and coefficient-of-restitution problems are especially reliable, repeated formats.
Related Chapters
- Work, Energy & Power
Elastic collisions rely directly on the kinetic energy conservation concept introduced in Work-Energy-Power.
- System of Particles & Rotational Motion
Centre of mass is the conceptual bridge into rigid-body rotational mechanics, which treats an object as a system of particles.
- Laws of Motion
Momentum conservation in collisions is a direct consequence of Newton's third law applied to a system of interacting bodies.
- Gravitation
Two-body gravitational problems are often analyzed relative to the system's centre of mass, the central concept of this chapter.
Frequently Asked Questions
What is the centre of mass, in simple terms?
It's the single point that represents the average position of a system's mass, weighted by how the mass is distributed. When you apply an external force to a system, the centre of mass moves exactly as if all the mass were concentrated at that one point.
What's the real difference between elastic and inelastic collisions?
In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, only momentum is conserved — some kinetic energy is converted to heat, sound, or deformation. A perfectly inelastic collision is the extreme case where the two objects stick together afterward.
Why can't I just apply Newton's second law to each object during a collision?
You technically could, but the force during a collision changes rapidly and is very hard to model directly. Momentum conservation sidesteps this entirely by looking only at the state before and after the collision, without needing to know what happened during it.
What is the coefficient of restitution?
It's a number between 0 and 1 that measures how 'bouncy' a collision is — the ratio of relative velocity of separation to relative velocity of approach. e=1 means perfectly elastic, e=0 means perfectly inelastic.
Does the centre of mass have to be located inside the object?
No. For irregular or hollow shapes, like a ring or a boomerang, the centre of mass can lie outside the physical material of the object entirely — it's a mathematical point, not necessarily a physical one.
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