Q.A motor cyclist (to be treated as a point mass) is to undertake horizontal circles inside the cylindrical wall of a well of inner radius 4 m. Coefficient of static friction between the tyres and the wall is 0.4. Calculate the minimum speed and frequency necessary to perform this stunt. (Use g = 10 m/s²)

In the well of death the wall's normal reaction supplies the centripetal force while friction balances the weight, giving $v_{min}=\sqrt{rg/\mu_s}$. …

A motorcyclist (treated as a point mass) undertakes horizontal circles inside a cylindrical well of inner radius r = 4 m, with coefficient of static friction $\mu_s=0.4$ between tyres and wall (use g = 10 m/s^2). Using $v_{min}=\sqrt{rg/\mu_s}=\sqrt{4\times10/0.4}=\sqrt{100}=10$ m/s, the corresponding minimum frequency follows from $n_{min}=v_{min}/(2\pi r)=10/(2\pi\times4)\approx0.4$ rev/s. The example fixes the pattern used throughout the rest of the well-of-death and banked-road problems: find the critical speed from the frictio …

Work with angular speed directly: $N=mr\omega^2$ and $\mu_s N\geq mg$ give $\omega_{min}=\sqrt{g/(\mu_s r)}=\sqrt{10/1.6}=2.5$ rad/s, so $v_{min}=r\o …

Writing the flat-road condition $v_{max}=\sqrt{\mu_s rg}$ here — the well of death has the OPPOSITE structure: friction balances weight (not the centripetal d …