The forces acting on the system
* gravitational force(mg)
* Normal force(v)
* Frictional force (f)
* Centrifugal force \((\frac{mv^2}r)\)
A system is in equilibrium is the rotational from of reference,
the net external force = net external torque = 0
(i) Torque = Due to gravitational force = ng AB
(ii) Torque - Due to centripetal force
= \(\frac{mv^2}r BC\)
Vc(T)net = 0 → Rotational equilibrium
-mg AB + \(\frac{mv^2}r BC\) = 0
mg AB = \(\frac{mv^2}r BC\)
From △ ABC,
AB = AC sin θ and BC = AC cos θ
mg AC sin θ = \(\frac{mv^2}r\)AC cos θ
tan θ = \(\frac{r}g\)
θ = tan-1\((\frac{v^2}{rg})\)
A cyclist has to bend by an angle θ from vertical θ = tan-1\((\frac{v^2}{rg})\) to stay in equilibrium and Hence to avoid falling.