The image represents road bank angle in circular motion.

To compute for the road bank angle, three essential parameters are needed and these parameters are **velocity (v), acceleration due to gravity (g) and radius (r).**

The formula for calculating the road bank angle;

θ = tan^{-1}(^{v²} / _{gr})

Where;

θ = Road Bank Angle

v = Velocity

g = Acceleration due to Gravity

r = Radius

Let’s solve an example;

Find the road bank angle where the acceleration due to gravity is 9.8, velocity is 35 and radius is 18.

This implies that;

v = Velocity = 35

g = Acceleration due to Gravity = 9.8

r = Radius = 18

θ = tan^{-1}(^{v²} / _{gr})

θ = tan^{-1}(^{35²} / _{(9.8)(18)})

θ = tan^{-1}(^{1225} / _{176.4})

θ = tan^{-1}(6.94)

θ = 81.81°

Therefore, the **road bank angle** is **81.81°.**

**Calculating the Velocity when Road Bank Angle, Acceleration due to Gravity and Radius is Given.**

v = √gr.tan θ

Where;

v = Velocity

θ = Road Bank Angle

g = Acceleration due to Gravity

r = Radius

Let’s solve an example;

Given that the road bank angle is 50, radius is 15 and acceleration due to gravity is 9.8. Find the velocity?

This implies that;

θ = Road Bank Angle = 50

g = Acceleration due to Gravity = 9.8

r = Radius = 15

v = √gr.tan θ

v = √(9.8 x 15)(tan 50)

v = √(147)(1.1917)

v = √175.1799

v = 13.235

Therefore, the **velocity** is **13.235.**