Rocket Propulsion
F_thrust = u(dm/dt) — rocket loses mass and gains velocity.
Key Notes
Rocket propulsion is a clean application of conservation of momentum: rocket ejects exhaust mass backward, gaining forward momentum.
Thrust F = u_e × (dm/dt), where u_e = exhaust velocity relative to rocket, dm/dt = mass-burning rate.
Tsiolkovsky rocket equation: Δv = u_e · ln(m_0/m_f), where m_0 = initial mass, m_f = final mass.
Δv determines mission feasibility. Reaching low Earth orbit: Δv ≈ 9-10 km/s.
Specific impulse I_sp = u_e/g₀ — measure of fuel efficiency. Chemical rockets: I_sp ≈ 300-450 s. Ion thrusters: ~3000+ s.
Mass ratio m_0/m_f determines how much velocity you can build up. Beyond ~10-20, structural and engineering limits dominate.
Multistaging (jettisoning empty fuel tanks) allows higher final Δv with reasonable mass ratios.
Newton's 3rd law in disguise: exhaust gas pushed backward ⇒ rocket pushed forward.
Formulas
Thrust (constant u_e)
Force from gas-momentum ejection rate.
Tsiolkovsky equation
Velocity change from initial mass m_0 to final m_f (no gravity / air resistance).
Specific impulse
Higher I_sp ⇒ more Δv per kg of fuel.
Variable-mass equation
With gravity term included.
Important Points
Rocket = continuous explosion. Conservation of momentum applied step-by-step gives Tsiolkovsky.
Doubling exhaust velocity DOUBLES Δv for the same fuel ratio. Better fuels = more efficient missions.
Mass ratio limit ~10-20 ⇒ for big Δv, need MULTISTAGE rockets (Saturn V had 3 stages).
Specific impulse I_sp is the rocket-engine industry's figure of merit. Higher I_sp = more delta-v per kg fuel.
Ion thrusters have very high I_sp but low thrust — slow but extremely fuel-efficient for deep space.
Rocket equation works in vacuum or atmosphere; air drag reduces effective Δv but the principle is identical.
Rocket Propulsion 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.