Linear Momentum
p = mv — momentum scales linearly with velocity; KE scales quadratically.
Key Notes
Linear momentum p of a particle: p = m·v. Vector quantity. Units: kg·m/s.
Newton's 2nd law (general form): F = dp/dt. For constant mass: F = m·a.
Total momentum of a system: P = Σ m_i·v_i.
Momentum of a SYSTEM = M·V_COM. So COM moves as if all momentum were a single point particle.
Conservation: if net external force = 0, total P is conserved.
Internal forces in a system change individual momenta but DO NOT change total momentum.
Photons have momentum p = h/λ (no rest mass).
Relativistic momentum: p = γmv = mv/√(1−v²/c²). Reduces to mv for v ≪ c.
Formulas
Momentum (definition)
Vector — has both magnitude and direction.
Newton's 2nd law (general)
Constant mass: F = ma. Variable mass (rockets): use this form.
Total momentum
Equals total mass × COM velocity.
Conservation
Conserved in any isolated system.
Relativistic momentum
Reduces to mv at low speeds.
Important Points
Momentum is a VECTOR — direction matters. 'Conservation of momentum' means each component is conserved.
Photons have p = h/λ even though m = 0 — relativistic energy-momentum: E² = (pc)² + (mc²)².
Newton's 2nd law in its more general form F = dp/dt captures variable-mass problems (rockets, conveyor belts).
Momentum is conserved in collisions WHETHER OR NOT energy is — that's why momentum is the more universal conservation law.
If you double speed, you double p. Double mass, you double p. Quadruple p means quadruple speed × mass.
p and KE are different things: p is linear in v, KE quadratic. Equal p can mean different KE.
Linear Momentum 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.