Momentum and Force

Momentum is mass × velocity (“amount of motion”). $p = mv \quad [\text{kg·m/s}]$

Force = rate of change of momentum (how much momentum changes per second): $F = \frac{\Delta(mv)}{\Delta t}$

Two ways to change momentum per second:

Way	Example	Force
① Same mass, change its speed	car accelerating	$F = m\,a$ (constant $m$)
② New mass every second gets a speed	throwing balls, wings pushing air down, water jet	$F = \dot m\, v$
Where it shows up:

• Lift: wings push $\dot m_{air} = \rho A_{lift} v$ down at $v_{lift}$ → $Mg = \dot m_{air} v_{lift}$
• Drag: same “mass swept per second” $\dot m = \rho A v$

Balance (no vertical acceleration → forces equal): floating boat $F_B = Mg$, level flight (= constant height) lift $= Mg$, hydrofoil at $v_{min}$ $F_{lift} = Mg$.

Related: Lift, Drag, Buoyancy. Archimedes’ principle