Momentum Conservation (Explosion)
Stationary body explodes into two — m₁v₁ + m₂v₂ = 0 demonstrated live.
Key Notes
Law of conservation of momentum: in an isolated system (no external force), total linear momentum is constant.
Derived from Newton's 3rd law: internal forces come in equal-and-opposite pairs, so they cancel in total.
In collisions: p_total before = p_total after, ALWAYS (whether elastic or not).
Components: P_x, P_y, P_z all conserved independently — pick axes wisely.
Useful for collisions, explosions, recoil problems (gun-bullet), rocket motion.
Conservation holds in any inertial reference frame; numerical values of P depend on frame, but conservation is universal.
Distinction from energy: momentum is ALWAYS conserved in collisions; kinetic energy is conserved only in ELASTIC collisions.
Photons carry momentum; conservation applies to atomic/nuclear reactions too.
Formulas
Conservation (general)
Total momentum invariant.
1D two-body collision
Initial → final velocities.
Recoil (gun-bullet)
Equal magnitudes, opposite directions; ratio = m_b/m_g.
Explosion (one body becomes many)
Pre-explosion momentum = sum of fragment momenta.
Important Points
Momentum conservation is THE most universal conservation law in classical mechanics — even more universal than KE conservation.
Pick axes: in 2D, x and y components are independently conserved. Use the symmetry of the problem.
Recoil of a gun is a direct application: bullet goes forward, gun goes backward, total p = 0.
Rocket thrust is also recoil: exhaust gas momentum equals (rocket mass) × Δv (in opposite direction).
Photons carry momentum p = hf/c — radiation pressure exists because photons impart momentum on absorption/reflection.
If frame is NON-INERTIAL: pseudo-forces act as external ⇒ momentum NOT conserved in that frame. Always pick an inertial frame.
Momentum Conservation (Explosion) notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.