Momentum is a measure of how much motion an object has. It is the product of mass and velocity: \$p = m\,v\$.
Think of it as the “push” an object carries when it moves.
🌟 Analogy: Imagine a bowling ball rolling down a hallway. The heavier the ball or the faster it rolls, the more momentum it has, so it’s harder to stop.
When an object moves through a fluid (air, water), it experiences a resistive (drag) force that grows with speed.
The drag force can be approximated by: \$F{\text{drag}} = \tfrac{1}{2}\,\rho\,C{\text{d}}\,A\,v^{2}\$,
where \$\rho\$ is fluid density, \$C_{\text{d}}\$ is the drag coefficient, \$A\$ is the cross‑sectional area, and \$v\$ is velocity.
As the object speeds up, \$F_{\text{drag}}\$ increases until it balances the weight \$mg\$. At that point, acceleration stops and the object falls at a constant speed – the terminal velocity.
Key Insight: Terminal velocity occurs when the net force is zero:
\$mg = \tfrac{1}{2}\,\rho\,C{\text{d}}\,A\,v{\text{t}}^{2}\$.
Solving for \$v_{\text{t}}\$ gives the speed at which the object stops accelerating.
| Property | Formula / Example |
|---|---|
| Momentum | \$p = m\,v\$ (e.g., 2 kg × 10 m/s = 20 kg·m/s) |
| Drag Force | \$F{\text{drag}} = \tfrac{1}{2}\,\rho\,C{\text{d}}\,A\,v^{2}\$ |
| Terminal Velocity | \$v{\text{t}} = \sqrt{\dfrac{2mg}{\rho\,C{\text{d}}\,A}}\$ |
🎉 Remember: When forces balance, motion becomes steady. Understanding how resistive forces work helps predict real‑world behaviours, from falling leaves to skydiving adventures!