Newton's Second Law & Momentum
$$\vec{F} = \frac{d\vec{p}}{dt} = m\vec{a}$$
Friction & Maximum Safe Speed on Banked Road:
- Static friction: $f_s \le \mu_s N$
- Optimum Speed on Banked Curve of Angle $\theta$:
$$v_0 = \sqrt{r g \tan\theta}$$
- Maximum Safe Speed with Friction $\mu$:
$$v_{\text{max}} = \sqrt{rg \left(\frac{\mu + \tan\theta}{1 - \mu\tan\theta}\right)}$$
