3 Questions around this concept.
A cyclist goes on a round a circular path with constant speed with 30m/s . If the radius of the path is 90m then the angle made by him with vertical will be:
A cyclist is moving with a velocity 20m/s. if he wants to take a circular turn of radius 40 m then for his safe turn what should be the value of angle made by the cyclist with vertical $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$
A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45°, the speed of the car is:

From figure.
$$
R \sin \theta=\frac{m v^2}{r}
$$
$$
R \cos \theta=m g
$$
(i) \& (ii)
$$
\begin{aligned}
& \tan \theta=\frac{v^2}{r g} \\
& \theta=\tan ^{-1}\left(\frac{v^2}{r g}\right)
\end{aligned}
$$
$V=$ velocity
$\mathbf{r}=$ radius of track
$\theta=$ angle with which cycle leans
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