Defined optimum speed.
Defined optimum speed.
The velocity of the vehicle on a circular balanced road is given by,
$v_{\max }=\left[r g\left(\frac{\mu_{s}+\tan \theta}{1-\mu_{s} \tan \theta}\right)\right]^{\frac{1}{2}}$
Here we have to take $\mu_{s}=0$ as the surface is smooth.
$v_{\max }=\left[\operatorname{rg}\left(\frac{0+\tan \theta}{1-0}\right)\right]^{\frac{1}{2}}$
$\therefore v_{\max } =\left[r g\left(\frac{\tan \theta}{1}\right)\right]^{-}$
$\therefore v_{\max } =\sqrt{r g \tan \theta}$
At this speed, frictional force is not needed at all to provide the necessary centripetal force. Driving at this speed on a banked road will cause little wear and tear on the tyres. $v_{0}$ is called the optimum speed.
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