Question

A cyclist is moving with a velocity v turns a circular path of radius r. His inclination with the vertical is given by

• A. $tan\theta =v^2/Rg$
• B. $sin\theta =v^2/Rg$
• C. $cos\theta =v^2/Rg$
• D. $cot\theta =v^2/Rg$

Answer 1

The correct option is A $tan\theta =v^2/Rg$

$N$ is the normal force.

Balancing the forces

$N\cos \theta =mg⟶\left(1\right)N\sin \theta =\frac{m{v}^2}{R}⟶\left(2\right)$

Dividing $\left(2\right)$ by$\left(1\right)$

$\tan \theta =\frac{v^2}{Rg}$