Center of Mass Revision Notes for NEET Physics PDF Download
🎯 CENTER OF MASS & COLLISIONS · COM
Center of mass • Motion of COM • Conservation of momentum • Elastic & Inelastic collisions • NEET problems
📍 CENTER OF MASS (COM)
Point where entire mass of a system can be assumed to be concentrated.
📐 For discrete particles
Rcm = (Σ mi ri) / Σ mi
For 2 particles: xcm = (m₁x₁ + m₂x₂)/(m₁ + m₂)
📏 For continuous body
rcm = (∫ r dm) / M
COM of common shapes:
Uniform rod: at center
Ring: at center (empty)
Disc: at center
Triangle: at centroid (1/3 height from base)
✏️ COM of two masses
🚀 MOTION OF CENTER OF MASS
Velocity of COM: Vcm = (Σ mi vi) / M
Acceleration of COM: Acm = (Σ Fext) / M
Conservation of momentum: If no external force, total momentum = constant → Vcm = constant.
💥 COLLISIONS
Two bodies collide, momentum is always conserved (if no external force). Energy may or may not be conserved.
🟢 Elastic Collision
KE conserved, momentum conserved.
For 1D: v₁' = [(m₁–m₂)v₁ + 2m₂v₂]/(m₁+m₂)
v₂' = [(m₂–m₁)v₂ + 2m₁v₁]/(m₁+m₂)
For equal masses: velocities exchange.
🔴 Inelastic Collision
KE not conserved, momentum conserved.
Perfectly inelastic: bodies stick together.
vcommon = (m₁v₁ + m₂v₂)/(m₁+m₂)
Loss in KE = ½ μ (v₁ – v₂)², where μ = reduced mass.
📏 Coefficient of Restitution (e)
e = (relative velocity after) / (relative velocity before) (for 1D).
e = 1 → elastic, e = 0 → perfectly inelastic, 0 < e < 1 → partially inelastic.
🖍️ Collision before & after (1D)
⚡ IMPULSE & SPECIAL COLLISIONS
Impulse = change in momentum = ∫ F dt = mΔv
Oblique collisions: Use components. For smooth surfaces, impulse is along common normal.
💡 NEET TIPS & SHORTCUTS
- COM of a system moves as if all external forces act at it and total mass is concentrated there.
- For two-body system, COM lies on line joining them, and m₁r₁ = m₂r₂ from COM.
- In perfectly inelastic collision, maximum KE loss occurs.
- For oblique collisions, resolve velocities along normal and tangential. Tangential component remains unchanged if no friction.
⚠️ COMMON MISTAKES
- Applying conservation of momentum when external forces are present.
- Assuming energy is conserved in inelastic collisions.
- Forgetting that COM can accelerate if external forces act.
- Using wrong sign for velocities in e formula.
📌 QUICK REVISION CARD
COM position: Rcm = Σ mi ri / M
Velocity of COM: Vcm = Σ mi vi / M
Momentum: P = M Vcm
Elastic 1D final velocities: given above
Perfectly inelastic common velocity: vf = (m₁v₁ + m₂v₂)/(m₁+m₂)
Coefficient of restitution: e = (v₂' – v₁')/(v₁ – v₂)