Question

A cyclist moves around a circular path of radius $39.2m$ with a speed of $19.6m/s$. He must lean inward at an angle $\theta$ with vertical given by

• A. $\theta =ta{n}^{-1}\left(1\right)$
• B. $\theta =ta{n}^{-1}\left(2\right)$
• C. $\theta =ta{n}^{-1}\left(3\right)$
• D. $\theta =ta{n}^{-1}\left(4\right)$

Answer 1

The correct option is A $\theta =ta{n}^{-1}\left(1\right)$

Let us suppose, he is leaned with an angle theta with vertical.
So the forces perpendicular to its cycle must balance.
Component of gravity: $mgsin\theta$
Component of centripetal force: $\frac{m{v}^2}{R}cos\theta$

$mgsin\theta =\frac{m{v}^2}{R}cos\theta$

$\Rightarrow tan\theta =\frac{19.6\times 19.6}{39.2\times 9.8}=1$

$\Rightarrow \theta ={tan}^{-1}\left(1\right)$