# Obtain an expression for the angle of lean when a cyclist takes a curved path

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Mass of cyclist + cycle = M

radius of curvature of th e curved path = R

ANgle of inclination from vertical = Ф

acceleration due to gravity = g

velocity of cyclist = v

Let the normal force : N from the ground on to cyclist. Balance forces in horizontal and vertical directions.

N sin Ф = M v² / R = centripetal force for the cyclist to move in a curve of radius R

N cos Ф = M g = weight balanced by normal reaction from ground

SO divide equ 1 by equ 2

Tan Ф = v² / Rg Ф = tan^-1 (v² / R g)

radius of curvature of th e curved path = R

ANgle of inclination from vertical = Ф

acceleration due to gravity = g

velocity of cyclist = v

Let the normal force : N from the ground on to cyclist. Balance forces in horizontal and vertical directions.

N sin Ф = M v² / R = centripetal force for the cyclist to move in a curve of radius R

N cos Ф = M g = weight balanced by normal reaction from ground

SO divide equ 1 by equ 2

Tan Ф = v² / Rg Ф = tan^-1 (v² / R g)